1,1,218,0,1.101495," ","integrate((b*x^2+a)*(d*x^2+c)*(f*x^2+e)^4,x, algorithm=""fricas"")","\frac{1}{13} x^{13} f^{4} d b + \frac{4}{11} x^{11} f^{3} e d b + \frac{1}{11} x^{11} f^{4} c b + \frac{1}{11} x^{11} f^{4} d a + \frac{2}{3} x^{9} f^{2} e^{2} d b + \frac{4}{9} x^{9} f^{3} e c b + \frac{4}{9} x^{9} f^{3} e d a + \frac{1}{9} x^{9} f^{4} c a + \frac{4}{7} x^{7} f e^{3} d b + \frac{6}{7} x^{7} f^{2} e^{2} c b + \frac{6}{7} x^{7} f^{2} e^{2} d a + \frac{4}{7} x^{7} f^{3} e c a + \frac{1}{5} x^{5} e^{4} d b + \frac{4}{5} x^{5} f e^{3} c b + \frac{4}{5} x^{5} f e^{3} d a + \frac{6}{5} x^{5} f^{2} e^{2} c a + \frac{1}{3} x^{3} e^{4} c b + \frac{1}{3} x^{3} e^{4} d a + \frac{4}{3} x^{3} f e^{3} c a + x e^{4} c a"," ",0,"1/13*x^13*f^4*d*b + 4/11*x^11*f^3*e*d*b + 1/11*x^11*f^4*c*b + 1/11*x^11*f^4*d*a + 2/3*x^9*f^2*e^2*d*b + 4/9*x^9*f^3*e*c*b + 4/9*x^9*f^3*e*d*a + 1/9*x^9*f^4*c*a + 4/7*x^7*f*e^3*d*b + 6/7*x^7*f^2*e^2*c*b + 6/7*x^7*f^2*e^2*d*a + 4/7*x^7*f^3*e*c*a + 1/5*x^5*e^4*d*b + 4/5*x^5*f*e^3*c*b + 4/5*x^5*f*e^3*d*a + 6/5*x^5*f^2*e^2*c*a + 1/3*x^3*e^4*c*b + 1/3*x^3*e^4*d*a + 4/3*x^3*f*e^3*c*a + x*e^4*c*a","A",0
2,1,165,0,1.073409," ","integrate((b*x^2+a)*(d*x^2+c)*(f*x^2+e)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} f^{3} d b + \frac{1}{3} x^{9} f^{2} e d b + \frac{1}{9} x^{9} f^{3} c b + \frac{1}{9} x^{9} f^{3} d a + \frac{3}{7} x^{7} f e^{2} d b + \frac{3}{7} x^{7} f^{2} e c b + \frac{3}{7} x^{7} f^{2} e d a + \frac{1}{7} x^{7} f^{3} c a + \frac{1}{5} x^{5} e^{3} d b + \frac{3}{5} x^{5} f e^{2} c b + \frac{3}{5} x^{5} f e^{2} d a + \frac{3}{5} x^{5} f^{2} e c a + \frac{1}{3} x^{3} e^{3} c b + \frac{1}{3} x^{3} e^{3} d a + x^{3} f e^{2} c a + x e^{3} c a"," ",0,"1/11*x^11*f^3*d*b + 1/3*x^9*f^2*e*d*b + 1/9*x^9*f^3*c*b + 1/9*x^9*f^3*d*a + 3/7*x^7*f*e^2*d*b + 3/7*x^7*f^2*e*c*b + 3/7*x^7*f^2*e*d*a + 1/7*x^7*f^3*c*a + 1/5*x^5*e^3*d*b + 3/5*x^5*f*e^2*c*b + 3/5*x^5*f*e^2*d*a + 3/5*x^5*f^2*e*c*a + 1/3*x^3*e^3*c*b + 1/3*x^3*e^3*d*a + x^3*f*e^2*c*a + x*e^3*c*a","A",0
3,1,114,0,1.171937," ","integrate((b*x^2+a)*(d*x^2+c)*(f*x^2+e)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} f^{2} d b + \frac{2}{7} x^{7} f e d b + \frac{1}{7} x^{7} f^{2} c b + \frac{1}{7} x^{7} f^{2} d a + \frac{1}{5} x^{5} e^{2} d b + \frac{2}{5} x^{5} f e c b + \frac{2}{5} x^{5} f e d a + \frac{1}{5} x^{5} f^{2} c a + \frac{1}{3} x^{3} e^{2} c b + \frac{1}{3} x^{3} e^{2} d a + \frac{2}{3} x^{3} f e c a + x e^{2} c a"," ",0,"1/9*x^9*f^2*d*b + 2/7*x^7*f*e*d*b + 1/7*x^7*f^2*c*b + 1/7*x^7*f^2*d*a + 1/5*x^5*e^2*d*b + 2/5*x^5*f*e*c*b + 2/5*x^5*f*e*d*a + 1/5*x^5*f^2*c*a + 1/3*x^3*e^2*c*b + 1/3*x^3*e^2*d*a + 2/3*x^3*f*e*c*a + x*e^2*c*a","A",0
4,1,62,0,0.629754," ","integrate((b*x^2+a)*(d*x^2+c)*(f*x^2+e),x, algorithm=""fricas"")","\frac{1}{7} x^{7} f d b + \frac{1}{5} x^{5} e d b + \frac{1}{5} x^{5} f c b + \frac{1}{5} x^{5} f d a + \frac{1}{3} x^{3} e c b + \frac{1}{3} x^{3} e d a + \frac{1}{3} x^{3} f c a + x e c a"," ",0,"1/7*x^7*f*d*b + 1/5*x^5*e*d*b + 1/5*x^5*f*c*b + 1/5*x^5*f*d*a + 1/3*x^3*e*c*b + 1/3*x^3*e*d*a + 1/3*x^3*f*c*a + x*e*c*a","A",0
5,1,191,0,1.422630," ","integrate((b*x^2+a)*(d*x^2+c)/(f*x^2+e),x, algorithm=""fricas"")","\left[\frac{2 \, b d e f^{2} x^{3} - 3 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) - 6 \, {\left(b d e^{2} f - {\left(b c + a d\right)} e f^{2}\right)} x}{6 \, e f^{3}}, \frac{b d e f^{2} x^{3} + 3 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) - 3 \, {\left(b d e^{2} f - {\left(b c + a d\right)} e f^{2}\right)} x}{3 \, e f^{3}}\right]"," ",0,"[1/6*(2*b*d*e*f^2*x^3 - 3*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) - 6*(b*d*e^2*f - (b*c + a*d)*e*f^2)*x)/(e*f^3), 1/3*(b*d*e*f^2*x^3 + 3*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) - 3*(b*d*e^2*f - (b*c + a*d)*e*f^2)*x)/(e*f^3)]","A",0
6,1,318,0,1.442934," ","integrate((b*x^2+a)*(d*x^2+c)/(f*x^2+e)^2,x, algorithm=""fricas"")","\left[\frac{4 \, b d e^{2} f^{2} x^{3} + {\left(3 \, b d e^{3} - a c e f^{2} - {\left(b c + a d\right)} e^{2} f + {\left(3 \, b d e^{2} f - a c f^{3} - {\left(b c + a d\right)} e f^{2}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) + 2 \, {\left(3 \, b d e^{3} f + a c e f^{3} - {\left(b c + a d\right)} e^{2} f^{2}\right)} x}{4 \, {\left(e^{2} f^{4} x^{2} + e^{3} f^{3}\right)}}, \frac{2 \, b d e^{2} f^{2} x^{3} - {\left(3 \, b d e^{3} - a c e f^{2} - {\left(b c + a d\right)} e^{2} f + {\left(3 \, b d e^{2} f - a c f^{3} - {\left(b c + a d\right)} e f^{2}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) + {\left(3 \, b d e^{3} f + a c e f^{3} - {\left(b c + a d\right)} e^{2} f^{2}\right)} x}{2 \, {\left(e^{2} f^{4} x^{2} + e^{3} f^{3}\right)}}\right]"," ",0,"[1/4*(4*b*d*e^2*f^2*x^3 + (3*b*d*e^3 - a*c*e*f^2 - (b*c + a*d)*e^2*f + (3*b*d*e^2*f - a*c*f^3 - (b*c + a*d)*e*f^2)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) + 2*(3*b*d*e^3*f + a*c*e*f^3 - (b*c + a*d)*e^2*f^2)*x)/(e^2*f^4*x^2 + e^3*f^3), 1/2*(2*b*d*e^2*f^2*x^3 - (3*b*d*e^3 - a*c*e*f^2 - (b*c + a*d)*e^2*f + (3*b*d*e^2*f - a*c*f^3 - (b*c + a*d)*e*f^2)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) + (3*b*d*e^3*f + a*c*e*f^3 - (b*c + a*d)*e^2*f^2)*x)/(e^2*f^4*x^2 + e^3*f^3)]","A",0
7,1,471,0,1.340936," ","integrate((b*x^2+a)*(d*x^2+c)/(f*x^2+e)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, b d e^{3} f^{2} - 3 \, a c e f^{4} - {\left(b c + a d\right)} e^{2} f^{3}\right)} x^{3} + {\left(3 \, b d e^{4} + 3 \, a c e^{2} f^{2} + {\left(b c + a d\right)} e^{3} f + {\left(3 \, b d e^{2} f^{2} + 3 \, a c f^{4} + {\left(b c + a d\right)} e f^{3}\right)} x^{4} + 2 \, {\left(3 \, b d e^{3} f + 3 \, a c e f^{3} + {\left(b c + a d\right)} e^{2} f^{2}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) + 2 \, {\left(3 \, b d e^{4} f - 5 \, a c e^{2} f^{3} + {\left(b c + a d\right)} e^{3} f^{2}\right)} x}{16 \, {\left(e^{3} f^{5} x^{4} + 2 \, e^{4} f^{4} x^{2} + e^{5} f^{3}\right)}}, -\frac{{\left(5 \, b d e^{3} f^{2} - 3 \, a c e f^{4} - {\left(b c + a d\right)} e^{2} f^{3}\right)} x^{3} - {\left(3 \, b d e^{4} + 3 \, a c e^{2} f^{2} + {\left(b c + a d\right)} e^{3} f + {\left(3 \, b d e^{2} f^{2} + 3 \, a c f^{4} + {\left(b c + a d\right)} e f^{3}\right)} x^{4} + 2 \, {\left(3 \, b d e^{3} f + 3 \, a c e f^{3} + {\left(b c + a d\right)} e^{2} f^{2}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) + {\left(3 \, b d e^{4} f - 5 \, a c e^{2} f^{3} + {\left(b c + a d\right)} e^{3} f^{2}\right)} x}{8 \, {\left(e^{3} f^{5} x^{4} + 2 \, e^{4} f^{4} x^{2} + e^{5} f^{3}\right)}}\right]"," ",0,"[-1/16*(2*(5*b*d*e^3*f^2 - 3*a*c*e*f^4 - (b*c + a*d)*e^2*f^3)*x^3 + (3*b*d*e^4 + 3*a*c*e^2*f^2 + (b*c + a*d)*e^3*f + (3*b*d*e^2*f^2 + 3*a*c*f^4 + (b*c + a*d)*e*f^3)*x^4 + 2*(3*b*d*e^3*f + 3*a*c*e*f^3 + (b*c + a*d)*e^2*f^2)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) + 2*(3*b*d*e^4*f - 5*a*c*e^2*f^3 + (b*c + a*d)*e^3*f^2)*x)/(e^3*f^5*x^4 + 2*e^4*f^4*x^2 + e^5*f^3), -1/8*((5*b*d*e^3*f^2 - 3*a*c*e*f^4 - (b*c + a*d)*e^2*f^3)*x^3 - (3*b*d*e^4 + 3*a*c*e^2*f^2 + (b*c + a*d)*e^3*f + (3*b*d*e^2*f^2 + 3*a*c*f^4 + (b*c + a*d)*e*f^3)*x^4 + 2*(3*b*d*e^3*f + 3*a*c*e*f^3 + (b*c + a*d)*e^2*f^2)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) + (3*b*d*e^4*f - 5*a*c*e^2*f^3 + (b*c + a*d)*e^3*f^2)*x)/(e^3*f^5*x^4 + 2*e^4*f^4*x^2 + e^5*f^3)]","A",0
8,1,642,0,1.466858," ","integrate((b*x^2+a)*(d*x^2+c)/(f*x^2+e)^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b d e^{3} f^{3} + 5 \, a c e f^{5} + {\left(b c + a d\right)} e^{2} f^{4}\right)} x^{5} - 16 \, {\left(b d e^{4} f^{2} - 5 \, a c e^{2} f^{4} - {\left(b c + a d\right)} e^{3} f^{3}\right)} x^{3} - 3 \, {\left(b d e^{5} + 5 \, a c e^{3} f^{2} + {\left(b d e^{2} f^{3} + 5 \, a c f^{5} + {\left(b c + a d\right)} e f^{4}\right)} x^{6} + {\left(b c + a d\right)} e^{4} f + 3 \, {\left(b d e^{3} f^{2} + 5 \, a c e f^{4} + {\left(b c + a d\right)} e^{2} f^{3}\right)} x^{4} + 3 \, {\left(b d e^{4} f + 5 \, a c e^{2} f^{3} + {\left(b c + a d\right)} e^{3} f^{2}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) - 6 \, {\left(b d e^{5} f - 11 \, a c e^{3} f^{3} + {\left(b c + a d\right)} e^{4} f^{2}\right)} x}{96 \, {\left(e^{4} f^{6} x^{6} + 3 \, e^{5} f^{5} x^{4} + 3 \, e^{6} f^{4} x^{2} + e^{7} f^{3}\right)}}, \frac{3 \, {\left(b d e^{3} f^{3} + 5 \, a c e f^{5} + {\left(b c + a d\right)} e^{2} f^{4}\right)} x^{5} - 8 \, {\left(b d e^{4} f^{2} - 5 \, a c e^{2} f^{4} - {\left(b c + a d\right)} e^{3} f^{3}\right)} x^{3} + 3 \, {\left(b d e^{5} + 5 \, a c e^{3} f^{2} + {\left(b d e^{2} f^{3} + 5 \, a c f^{5} + {\left(b c + a d\right)} e f^{4}\right)} x^{6} + {\left(b c + a d\right)} e^{4} f + 3 \, {\left(b d e^{3} f^{2} + 5 \, a c e f^{4} + {\left(b c + a d\right)} e^{2} f^{3}\right)} x^{4} + 3 \, {\left(b d e^{4} f + 5 \, a c e^{2} f^{3} + {\left(b c + a d\right)} e^{3} f^{2}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) - 3 \, {\left(b d e^{5} f - 11 \, a c e^{3} f^{3} + {\left(b c + a d\right)} e^{4} f^{2}\right)} x}{48 \, {\left(e^{4} f^{6} x^{6} + 3 \, e^{5} f^{5} x^{4} + 3 \, e^{6} f^{4} x^{2} + e^{7} f^{3}\right)}}\right]"," ",0,"[1/96*(6*(b*d*e^3*f^3 + 5*a*c*e*f^5 + (b*c + a*d)*e^2*f^4)*x^5 - 16*(b*d*e^4*f^2 - 5*a*c*e^2*f^4 - (b*c + a*d)*e^3*f^3)*x^3 - 3*(b*d*e^5 + 5*a*c*e^3*f^2 + (b*d*e^2*f^3 + 5*a*c*f^5 + (b*c + a*d)*e*f^4)*x^6 + (b*c + a*d)*e^4*f + 3*(b*d*e^3*f^2 + 5*a*c*e*f^4 + (b*c + a*d)*e^2*f^3)*x^4 + 3*(b*d*e^4*f + 5*a*c*e^2*f^3 + (b*c + a*d)*e^3*f^2)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) - 6*(b*d*e^5*f - 11*a*c*e^3*f^3 + (b*c + a*d)*e^4*f^2)*x)/(e^4*f^6*x^6 + 3*e^5*f^5*x^4 + 3*e^6*f^4*x^2 + e^7*f^3), 1/48*(3*(b*d*e^3*f^3 + 5*a*c*e*f^5 + (b*c + a*d)*e^2*f^4)*x^5 - 8*(b*d*e^4*f^2 - 5*a*c*e^2*f^4 - (b*c + a*d)*e^3*f^3)*x^3 + 3*(b*d*e^5 + 5*a*c*e^3*f^2 + (b*d*e^2*f^3 + 5*a*c*f^5 + (b*c + a*d)*e*f^4)*x^6 + (b*c + a*d)*e^4*f + 3*(b*d*e^3*f^2 + 5*a*c*e*f^4 + (b*c + a*d)*e^2*f^3)*x^4 + 3*(b*d*e^4*f + 5*a*c*e^2*f^3 + (b*c + a*d)*e^3*f^2)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) - 3*(b*d*e^5*f - 11*a*c*e^3*f^3 + (b*c + a*d)*e^4*f^2)*x)/(e^4*f^6*x^6 + 3*e^5*f^5*x^4 + 3*e^6*f^4*x^2 + e^7*f^3)]","B",0
9,1,289,0,1.164320," ","integrate((b*x^2+a)*(d*x^2+c)^2*(f*x^2+e)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} f^{3} d^{2} b + \frac{3}{11} x^{11} f^{2} e d^{2} b + \frac{2}{11} x^{11} f^{3} d c b + \frac{1}{11} x^{11} f^{3} d^{2} a + \frac{1}{3} x^{9} f e^{2} d^{2} b + \frac{2}{3} x^{9} f^{2} e d c b + \frac{1}{9} x^{9} f^{3} c^{2} b + \frac{1}{3} x^{9} f^{2} e d^{2} a + \frac{2}{9} x^{9} f^{3} d c a + \frac{1}{7} x^{7} e^{3} d^{2} b + \frac{6}{7} x^{7} f e^{2} d c b + \frac{3}{7} x^{7} f^{2} e c^{2} b + \frac{3}{7} x^{7} f e^{2} d^{2} a + \frac{6}{7} x^{7} f^{2} e d c a + \frac{1}{7} x^{7} f^{3} c^{2} a + \frac{2}{5} x^{5} e^{3} d c b + \frac{3}{5} x^{5} f e^{2} c^{2} b + \frac{1}{5} x^{5} e^{3} d^{2} a + \frac{6}{5} x^{5} f e^{2} d c a + \frac{3}{5} x^{5} f^{2} e c^{2} a + \frac{1}{3} x^{3} e^{3} c^{2} b + \frac{2}{3} x^{3} e^{3} d c a + x^{3} f e^{2} c^{2} a + x e^{3} c^{2} a"," ",0,"1/13*x^13*f^3*d^2*b + 3/11*x^11*f^2*e*d^2*b + 2/11*x^11*f^3*d*c*b + 1/11*x^11*f^3*d^2*a + 1/3*x^9*f*e^2*d^2*b + 2/3*x^9*f^2*e*d*c*b + 1/9*x^9*f^3*c^2*b + 1/3*x^9*f^2*e*d^2*a + 2/9*x^9*f^3*d*c*a + 1/7*x^7*e^3*d^2*b + 6/7*x^7*f*e^2*d*c*b + 3/7*x^7*f^2*e*c^2*b + 3/7*x^7*f*e^2*d^2*a + 6/7*x^7*f^2*e*d*c*a + 1/7*x^7*f^3*c^2*a + 2/5*x^5*e^3*d*c*b + 3/5*x^5*f*e^2*c^2*b + 1/5*x^5*e^3*d^2*a + 6/5*x^5*f*e^2*d*c*a + 3/5*x^5*f^2*e*c^2*a + 1/3*x^3*e^3*c^2*b + 2/3*x^3*e^3*d*c*a + x^3*f*e^2*c^2*a + x*e^3*c^2*a","A",0
10,1,202,0,0.870777," ","integrate((b*x^2+a)*(d*x^2+c)^2*(f*x^2+e)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} f^{2} d^{2} b + \frac{2}{9} x^{9} f e d^{2} b + \frac{2}{9} x^{9} f^{2} d c b + \frac{1}{9} x^{9} f^{2} d^{2} a + \frac{1}{7} x^{7} e^{2} d^{2} b + \frac{4}{7} x^{7} f e d c b + \frac{1}{7} x^{7} f^{2} c^{2} b + \frac{2}{7} x^{7} f e d^{2} a + \frac{2}{7} x^{7} f^{2} d c a + \frac{2}{5} x^{5} e^{2} d c b + \frac{2}{5} x^{5} f e c^{2} b + \frac{1}{5} x^{5} e^{2} d^{2} a + \frac{4}{5} x^{5} f e d c a + \frac{1}{5} x^{5} f^{2} c^{2} a + \frac{1}{3} x^{3} e^{2} c^{2} b + \frac{2}{3} x^{3} e^{2} d c a + \frac{2}{3} x^{3} f e c^{2} a + x e^{2} c^{2} a"," ",0,"1/11*x^11*f^2*d^2*b + 2/9*x^9*f*e*d^2*b + 2/9*x^9*f^2*d*c*b + 1/9*x^9*f^2*d^2*a + 1/7*x^7*e^2*d^2*b + 4/7*x^7*f*e*d*c*b + 1/7*x^7*f^2*c^2*b + 2/7*x^7*f*e*d^2*a + 2/7*x^7*f^2*d*c*a + 2/5*x^5*e^2*d*c*b + 2/5*x^5*f*e*c^2*b + 1/5*x^5*e^2*d^2*a + 4/5*x^5*f*e*d*c*a + 1/5*x^5*f^2*c^2*a + 1/3*x^3*e^2*c^2*b + 2/3*x^3*e^2*d*c*a + 2/3*x^3*f*e*c^2*a + x*e^2*c^2*a","A",0
11,1,114,0,1.048205," ","integrate((b*x^2+a)*(d*x^2+c)^2*(f*x^2+e),x, algorithm=""fricas"")","\frac{1}{9} x^{9} f d^{2} b + \frac{1}{7} x^{7} e d^{2} b + \frac{2}{7} x^{7} f d c b + \frac{1}{7} x^{7} f d^{2} a + \frac{2}{5} x^{5} e d c b + \frac{1}{5} x^{5} f c^{2} b + \frac{1}{5} x^{5} e d^{2} a + \frac{2}{5} x^{5} f d c a + \frac{1}{3} x^{3} e c^{2} b + \frac{2}{3} x^{3} e d c a + \frac{1}{3} x^{3} f c^{2} a + x e c^{2} a"," ",0,"1/9*x^9*f*d^2*b + 1/7*x^7*e*d^2*b + 2/7*x^7*f*d*c*b + 1/7*x^7*f*d^2*a + 2/5*x^5*e*d*c*b + 1/5*x^5*f*c^2*b + 1/5*x^5*e*d^2*a + 2/5*x^5*f*d*c*a + 1/3*x^3*e*c^2*b + 2/3*x^3*e*d*c*a + 1/3*x^3*f*c^2*a + x*e*c^2*a","A",0
12,1,366,0,1.194647," ","integrate((b*x^2+a)*(d*x^2+c)^2/(f*x^2+e),x, algorithm=""fricas"")","\left[\frac{6 \, b d^{2} e f^{3} x^{5} - 10 \, {\left(b d^{2} e^{2} f^{2} - {\left(2 \, b c d + a d^{2}\right)} e f^{3}\right)} x^{3} + 15 \, {\left(b d^{2} e^{3} - a c^{2} f^{3} - {\left(2 \, b c d + a d^{2}\right)} e^{2} f + {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) + 30 \, {\left(b d^{2} e^{3} f - {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e f^{3}\right)} x}{30 \, e f^{4}}, \frac{3 \, b d^{2} e f^{3} x^{5} - 5 \, {\left(b d^{2} e^{2} f^{2} - {\left(2 \, b c d + a d^{2}\right)} e f^{3}\right)} x^{3} - 15 \, {\left(b d^{2} e^{3} - a c^{2} f^{3} - {\left(2 \, b c d + a d^{2}\right)} e^{2} f + {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) + 15 \, {\left(b d^{2} e^{3} f - {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e f^{3}\right)} x}{15 \, e f^{4}}\right]"," ",0,"[1/30*(6*b*d^2*e*f^3*x^5 - 10*(b*d^2*e^2*f^2 - (2*b*c*d + a*d^2)*e*f^3)*x^3 + 15*(b*d^2*e^3 - a*c^2*f^3 - (2*b*c*d + a*d^2)*e^2*f + (b*c^2 + 2*a*c*d)*e*f^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) + 30*(b*d^2*e^3*f - (2*b*c*d + a*d^2)*e^2*f^2 + (b*c^2 + 2*a*c*d)*e*f^3)*x)/(e*f^4), 1/15*(3*b*d^2*e*f^3*x^5 - 5*(b*d^2*e^2*f^2 - (2*b*c*d + a*d^2)*e*f^3)*x^3 - 15*(b*d^2*e^3 - a*c^2*f^3 - (2*b*c*d + a*d^2)*e^2*f + (b*c^2 + 2*a*c*d)*e*f^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) + 15*(b*d^2*e^3*f - (2*b*c*d + a*d^2)*e^2*f^2 + (b*c^2 + 2*a*c*d)*e*f^3)*x)/(e*f^4)]","A",0
13,1,552,0,1.382084," ","integrate((b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^2,x, algorithm=""fricas"")","\left[\frac{4 \, b d^{2} e^{2} f^{3} x^{5} - 4 \, {\left(5 \, b d^{2} e^{3} f^{2} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{3}\right)} x^{3} - 3 \, {\left(5 \, b d^{2} e^{4} + a c^{2} e f^{3} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{3} f + {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{2} + {\left(5 \, b d^{2} e^{3} f + a c^{2} f^{4} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e f^{3}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) - 6 \, {\left(5 \, b d^{2} e^{4} f - a c^{2} e f^{4} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{3}\right)} x}{12 \, {\left(e^{2} f^{5} x^{2} + e^{3} f^{4}\right)}}, \frac{2 \, b d^{2} e^{2} f^{3} x^{5} - 2 \, {\left(5 \, b d^{2} e^{3} f^{2} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{3}\right)} x^{3} + 3 \, {\left(5 \, b d^{2} e^{4} + a c^{2} e f^{3} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{3} f + {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{2} + {\left(5 \, b d^{2} e^{3} f + a c^{2} f^{4} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e f^{3}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) - 3 \, {\left(5 \, b d^{2} e^{4} f - a c^{2} e f^{4} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{3}\right)} x}{6 \, {\left(e^{2} f^{5} x^{2} + e^{3} f^{4}\right)}}\right]"," ",0,"[1/12*(4*b*d^2*e^2*f^3*x^5 - 4*(5*b*d^2*e^3*f^2 - 3*(2*b*c*d + a*d^2)*e^2*f^3)*x^3 - 3*(5*b*d^2*e^4 + a*c^2*e*f^3 - 3*(2*b*c*d + a*d^2)*e^3*f + (b*c^2 + 2*a*c*d)*e^2*f^2 + (5*b*d^2*e^3*f + a*c^2*f^4 - 3*(2*b*c*d + a*d^2)*e^2*f^2 + (b*c^2 + 2*a*c*d)*e*f^3)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) - 6*(5*b*d^2*e^4*f - a*c^2*e*f^4 - 3*(2*b*c*d + a*d^2)*e^3*f^2 + (b*c^2 + 2*a*c*d)*e^2*f^3)*x)/(e^2*f^5*x^2 + e^3*f^4), 1/6*(2*b*d^2*e^2*f^3*x^5 - 2*(5*b*d^2*e^3*f^2 - 3*(2*b*c*d + a*d^2)*e^2*f^3)*x^3 + 3*(5*b*d^2*e^4 + a*c^2*e*f^3 - 3*(2*b*c*d + a*d^2)*e^3*f + (b*c^2 + 2*a*c*d)*e^2*f^2 + (5*b*d^2*e^3*f + a*c^2*f^4 - 3*(2*b*c*d + a*d^2)*e^2*f^2 + (b*c^2 + 2*a*c*d)*e*f^3)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) - 3*(5*b*d^2*e^4*f - a*c^2*e*f^4 - 3*(2*b*c*d + a*d^2)*e^3*f^2 + (b*c^2 + 2*a*c*d)*e^2*f^3)*x)/(e^2*f^5*x^2 + e^3*f^4)]","A",0
14,1,777,0,1.425522," ","integrate((b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^3,x, algorithm=""fricas"")","\left[\frac{16 \, b d^{2} e^{3} f^{3} x^{5} + 2 \, {\left(25 \, b d^{2} e^{4} f^{2} + 3 \, a c^{2} e f^{5} - 5 \, {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{3} + {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{4}\right)} x^{3} + {\left(15 \, b d^{2} e^{5} - 3 \, a c^{2} e^{2} f^{3} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{4} f - {\left(b c^{2} + 2 \, a c d\right)} e^{3} f^{2} + {\left(15 \, b d^{2} e^{3} f^{2} - 3 \, a c^{2} f^{5} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{3} - {\left(b c^{2} + 2 \, a c d\right)} e f^{4}\right)} x^{4} + 2 \, {\left(15 \, b d^{2} e^{4} f - 3 \, a c^{2} e f^{4} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{2} - {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{3}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) + 2 \, {\left(15 \, b d^{2} e^{5} f + 5 \, a c^{2} e^{2} f^{4} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{4} f^{2} - {\left(b c^{2} + 2 \, a c d\right)} e^{3} f^{3}\right)} x}{16 \, {\left(e^{3} f^{6} x^{4} + 2 \, e^{4} f^{5} x^{2} + e^{5} f^{4}\right)}}, \frac{8 \, b d^{2} e^{3} f^{3} x^{5} + {\left(25 \, b d^{2} e^{4} f^{2} + 3 \, a c^{2} e f^{5} - 5 \, {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{3} + {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{4}\right)} x^{3} - {\left(15 \, b d^{2} e^{5} - 3 \, a c^{2} e^{2} f^{3} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{4} f - {\left(b c^{2} + 2 \, a c d\right)} e^{3} f^{2} + {\left(15 \, b d^{2} e^{3} f^{2} - 3 \, a c^{2} f^{5} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{3} - {\left(b c^{2} + 2 \, a c d\right)} e f^{4}\right)} x^{4} + 2 \, {\left(15 \, b d^{2} e^{4} f - 3 \, a c^{2} e f^{4} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{2} - {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{3}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) + {\left(15 \, b d^{2} e^{5} f + 5 \, a c^{2} e^{2} f^{4} - 3 \, {\left(2 \, b c d + a d^{2}\right)} e^{4} f^{2} - {\left(b c^{2} + 2 \, a c d\right)} e^{3} f^{3}\right)} x}{8 \, {\left(e^{3} f^{6} x^{4} + 2 \, e^{4} f^{5} x^{2} + e^{5} f^{4}\right)}}\right]"," ",0,"[1/16*(16*b*d^2*e^3*f^3*x^5 + 2*(25*b*d^2*e^4*f^2 + 3*a*c^2*e*f^5 - 5*(2*b*c*d + a*d^2)*e^3*f^3 + (b*c^2 + 2*a*c*d)*e^2*f^4)*x^3 + (15*b*d^2*e^5 - 3*a*c^2*e^2*f^3 - 3*(2*b*c*d + a*d^2)*e^4*f - (b*c^2 + 2*a*c*d)*e^3*f^2 + (15*b*d^2*e^3*f^2 - 3*a*c^2*f^5 - 3*(2*b*c*d + a*d^2)*e^2*f^3 - (b*c^2 + 2*a*c*d)*e*f^4)*x^4 + 2*(15*b*d^2*e^4*f - 3*a*c^2*e*f^4 - 3*(2*b*c*d + a*d^2)*e^3*f^2 - (b*c^2 + 2*a*c*d)*e^2*f^3)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) + 2*(15*b*d^2*e^5*f + 5*a*c^2*e^2*f^4 - 3*(2*b*c*d + a*d^2)*e^4*f^2 - (b*c^2 + 2*a*c*d)*e^3*f^3)*x)/(e^3*f^6*x^4 + 2*e^4*f^5*x^2 + e^5*f^4), 1/8*(8*b*d^2*e^3*f^3*x^5 + (25*b*d^2*e^4*f^2 + 3*a*c^2*e*f^5 - 5*(2*b*c*d + a*d^2)*e^3*f^3 + (b*c^2 + 2*a*c*d)*e^2*f^4)*x^3 - (15*b*d^2*e^5 - 3*a*c^2*e^2*f^3 - 3*(2*b*c*d + a*d^2)*e^4*f - (b*c^2 + 2*a*c*d)*e^3*f^2 + (15*b*d^2*e^3*f^2 - 3*a*c^2*f^5 - 3*(2*b*c*d + a*d^2)*e^2*f^3 - (b*c^2 + 2*a*c*d)*e*f^4)*x^4 + 2*(15*b*d^2*e^4*f - 3*a*c^2*e*f^4 - 3*(2*b*c*d + a*d^2)*e^3*f^2 - (b*c^2 + 2*a*c*d)*e^2*f^3)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) + (15*b*d^2*e^5*f + 5*a*c^2*e^2*f^4 - 3*(2*b*c*d + a*d^2)*e^4*f^2 - (b*c^2 + 2*a*c*d)*e^3*f^3)*x)/(e^3*f^6*x^4 + 2*e^4*f^5*x^2 + e^5*f^4)]","A",0
15,1,1024,0,1.117666," ","integrate((b*x^2+a)*(d*x^2+c)^2/(f*x^2+e)^4,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(11 \, b d^{2} e^{4} f^{3} - 5 \, a c^{2} e f^{6} - {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{4} - {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{5}\right)} x^{5} + 16 \, {\left(5 \, b d^{2} e^{5} f^{2} - 5 \, a c^{2} e^{2} f^{5} + {\left(2 \, b c d + a d^{2}\right)} e^{4} f^{3} - {\left(b c^{2} + 2 \, a c d\right)} e^{3} f^{4}\right)} x^{3} + 3 \, {\left(5 \, b d^{2} e^{6} + 5 \, a c^{2} e^{3} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{5} f + {\left(b c^{2} + 2 \, a c d\right)} e^{4} f^{2} + {\left(5 \, b d^{2} e^{3} f^{3} + 5 \, a c^{2} f^{6} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{4} + {\left(b c^{2} + 2 \, a c d\right)} e f^{5}\right)} x^{6} + 3 \, {\left(5 \, b d^{2} e^{4} f^{2} + 5 \, a c^{2} e f^{5} + {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{3} + {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{4}\right)} x^{4} + 3 \, {\left(5 \, b d^{2} e^{5} f + 5 \, a c^{2} e^{2} f^{4} + {\left(2 \, b c d + a d^{2}\right)} e^{4} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e^{3} f^{3}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) + 6 \, {\left(5 \, b d^{2} e^{6} f - 11 \, a c^{2} e^{3} f^{4} + {\left(2 \, b c d + a d^{2}\right)} e^{5} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e^{4} f^{3}\right)} x}{96 \, {\left(e^{4} f^{7} x^{6} + 3 \, e^{5} f^{6} x^{4} + 3 \, e^{6} f^{5} x^{2} + e^{7} f^{4}\right)}}, -\frac{3 \, {\left(11 \, b d^{2} e^{4} f^{3} - 5 \, a c^{2} e f^{6} - {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{4} - {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{5}\right)} x^{5} + 8 \, {\left(5 \, b d^{2} e^{5} f^{2} - 5 \, a c^{2} e^{2} f^{5} + {\left(2 \, b c d + a d^{2}\right)} e^{4} f^{3} - {\left(b c^{2} + 2 \, a c d\right)} e^{3} f^{4}\right)} x^{3} - 3 \, {\left(5 \, b d^{2} e^{6} + 5 \, a c^{2} e^{3} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{5} f + {\left(b c^{2} + 2 \, a c d\right)} e^{4} f^{2} + {\left(5 \, b d^{2} e^{3} f^{3} + 5 \, a c^{2} f^{6} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{4} + {\left(b c^{2} + 2 \, a c d\right)} e f^{5}\right)} x^{6} + 3 \, {\left(5 \, b d^{2} e^{4} f^{2} + 5 \, a c^{2} e f^{5} + {\left(2 \, b c d + a d^{2}\right)} e^{3} f^{3} + {\left(b c^{2} + 2 \, a c d\right)} e^{2} f^{4}\right)} x^{4} + 3 \, {\left(5 \, b d^{2} e^{5} f + 5 \, a c^{2} e^{2} f^{4} + {\left(2 \, b c d + a d^{2}\right)} e^{4} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e^{3} f^{3}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) + 3 \, {\left(5 \, b d^{2} e^{6} f - 11 \, a c^{2} e^{3} f^{4} + {\left(2 \, b c d + a d^{2}\right)} e^{5} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e^{4} f^{3}\right)} x}{48 \, {\left(e^{4} f^{7} x^{6} + 3 \, e^{5} f^{6} x^{4} + 3 \, e^{6} f^{5} x^{2} + e^{7} f^{4}\right)}}\right]"," ",0,"[-1/96*(6*(11*b*d^2*e^4*f^3 - 5*a*c^2*e*f^6 - (2*b*c*d + a*d^2)*e^3*f^4 - (b*c^2 + 2*a*c*d)*e^2*f^5)*x^5 + 16*(5*b*d^2*e^5*f^2 - 5*a*c^2*e^2*f^5 + (2*b*c*d + a*d^2)*e^4*f^3 - (b*c^2 + 2*a*c*d)*e^3*f^4)*x^3 + 3*(5*b*d^2*e^6 + 5*a*c^2*e^3*f^3 + (2*b*c*d + a*d^2)*e^5*f + (b*c^2 + 2*a*c*d)*e^4*f^2 + (5*b*d^2*e^3*f^3 + 5*a*c^2*f^6 + (2*b*c*d + a*d^2)*e^2*f^4 + (b*c^2 + 2*a*c*d)*e*f^5)*x^6 + 3*(5*b*d^2*e^4*f^2 + 5*a*c^2*e*f^5 + (2*b*c*d + a*d^2)*e^3*f^3 + (b*c^2 + 2*a*c*d)*e^2*f^4)*x^4 + 3*(5*b*d^2*e^5*f + 5*a*c^2*e^2*f^4 + (2*b*c*d + a*d^2)*e^4*f^2 + (b*c^2 + 2*a*c*d)*e^3*f^3)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) + 6*(5*b*d^2*e^6*f - 11*a*c^2*e^3*f^4 + (2*b*c*d + a*d^2)*e^5*f^2 + (b*c^2 + 2*a*c*d)*e^4*f^3)*x)/(e^4*f^7*x^6 + 3*e^5*f^6*x^4 + 3*e^6*f^5*x^2 + e^7*f^4), -1/48*(3*(11*b*d^2*e^4*f^3 - 5*a*c^2*e*f^6 - (2*b*c*d + a*d^2)*e^3*f^4 - (b*c^2 + 2*a*c*d)*e^2*f^5)*x^5 + 8*(5*b*d^2*e^5*f^2 - 5*a*c^2*e^2*f^5 + (2*b*c*d + a*d^2)*e^4*f^3 - (b*c^2 + 2*a*c*d)*e^3*f^4)*x^3 - 3*(5*b*d^2*e^6 + 5*a*c^2*e^3*f^3 + (2*b*c*d + a*d^2)*e^5*f + (b*c^2 + 2*a*c*d)*e^4*f^2 + (5*b*d^2*e^3*f^3 + 5*a*c^2*f^6 + (2*b*c*d + a*d^2)*e^2*f^4 + (b*c^2 + 2*a*c*d)*e*f^5)*x^6 + 3*(5*b*d^2*e^4*f^2 + 5*a*c^2*e*f^5 + (2*b*c*d + a*d^2)*e^3*f^3 + (b*c^2 + 2*a*c*d)*e^2*f^4)*x^4 + 3*(5*b*d^2*e^5*f + 5*a*c^2*e^2*f^4 + (2*b*c*d + a*d^2)*e^4*f^2 + (b*c^2 + 2*a*c*d)*e^3*f^3)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) + 3*(5*b*d^2*e^6*f - 11*a*c^2*e^3*f^4 + (2*b*c*d + a*d^2)*e^5*f^2 + (b*c^2 + 2*a*c*d)*e^4*f^3)*x)/(e^4*f^7*x^6 + 3*e^5*f^6*x^4 + 3*e^6*f^5*x^2 + e^7*f^4)]","B",0
16,1,409,0,1.209288," ","integrate((b*x^2+a)*(d*x^2+c)^3*(f*x^2+e)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} f^{3} d^{3} b + \frac{3}{13} x^{13} f^{2} e d^{3} b + \frac{3}{13} x^{13} f^{3} d^{2} c b + \frac{1}{13} x^{13} f^{3} d^{3} a + \frac{3}{11} x^{11} f e^{2} d^{3} b + \frac{9}{11} x^{11} f^{2} e d^{2} c b + \frac{3}{11} x^{11} f^{3} d c^{2} b + \frac{3}{11} x^{11} f^{2} e d^{3} a + \frac{3}{11} x^{11} f^{3} d^{2} c a + \frac{1}{9} x^{9} e^{3} d^{3} b + x^{9} f e^{2} d^{2} c b + x^{9} f^{2} e d c^{2} b + \frac{1}{9} x^{9} f^{3} c^{3} b + \frac{1}{3} x^{9} f e^{2} d^{3} a + x^{9} f^{2} e d^{2} c a + \frac{1}{3} x^{9} f^{3} d c^{2} a + \frac{3}{7} x^{7} e^{3} d^{2} c b + \frac{9}{7} x^{7} f e^{2} d c^{2} b + \frac{3}{7} x^{7} f^{2} e c^{3} b + \frac{1}{7} x^{7} e^{3} d^{3} a + \frac{9}{7} x^{7} f e^{2} d^{2} c a + \frac{9}{7} x^{7} f^{2} e d c^{2} a + \frac{1}{7} x^{7} f^{3} c^{3} a + \frac{3}{5} x^{5} e^{3} d c^{2} b + \frac{3}{5} x^{5} f e^{2} c^{3} b + \frac{3}{5} x^{5} e^{3} d^{2} c a + \frac{9}{5} x^{5} f e^{2} d c^{2} a + \frac{3}{5} x^{5} f^{2} e c^{3} a + \frac{1}{3} x^{3} e^{3} c^{3} b + x^{3} e^{3} d c^{2} a + x^{3} f e^{2} c^{3} a + x e^{3} c^{3} a"," ",0,"1/15*x^15*f^3*d^3*b + 3/13*x^13*f^2*e*d^3*b + 3/13*x^13*f^3*d^2*c*b + 1/13*x^13*f^3*d^3*a + 3/11*x^11*f*e^2*d^3*b + 9/11*x^11*f^2*e*d^2*c*b + 3/11*x^11*f^3*d*c^2*b + 3/11*x^11*f^2*e*d^3*a + 3/11*x^11*f^3*d^2*c*a + 1/9*x^9*e^3*d^3*b + x^9*f*e^2*d^2*c*b + x^9*f^2*e*d*c^2*b + 1/9*x^9*f^3*c^3*b + 1/3*x^9*f*e^2*d^3*a + x^9*f^2*e*d^2*c*a + 1/3*x^9*f^3*d*c^2*a + 3/7*x^7*e^3*d^2*c*b + 9/7*x^7*f*e^2*d*c^2*b + 3/7*x^7*f^2*e*c^3*b + 1/7*x^7*e^3*d^3*a + 9/7*x^7*f*e^2*d^2*c*a + 9/7*x^7*f^2*e*d*c^2*a + 1/7*x^7*f^3*c^3*a + 3/5*x^5*e^3*d*c^2*b + 3/5*x^5*f*e^2*c^3*b + 3/5*x^5*e^3*d^2*c*a + 9/5*x^5*f*e^2*d*c^2*a + 3/5*x^5*f^2*e*c^3*a + 1/3*x^3*e^3*c^3*b + x^3*e^3*d*c^2*a + x^3*f*e^2*c^3*a + x*e^3*c^3*a","A",0
17,1,289,0,1.222809," ","integrate((b*x^2+a)*(d*x^2+c)^3*(f*x^2+e)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} f^{2} d^{3} b + \frac{2}{11} x^{11} f e d^{3} b + \frac{3}{11} x^{11} f^{2} d^{2} c b + \frac{1}{11} x^{11} f^{2} d^{3} a + \frac{1}{9} x^{9} e^{2} d^{3} b + \frac{2}{3} x^{9} f e d^{2} c b + \frac{1}{3} x^{9} f^{2} d c^{2} b + \frac{2}{9} x^{9} f e d^{3} a + \frac{1}{3} x^{9} f^{2} d^{2} c a + \frac{3}{7} x^{7} e^{2} d^{2} c b + \frac{6}{7} x^{7} f e d c^{2} b + \frac{1}{7} x^{7} f^{2} c^{3} b + \frac{1}{7} x^{7} e^{2} d^{3} a + \frac{6}{7} x^{7} f e d^{2} c a + \frac{3}{7} x^{7} f^{2} d c^{2} a + \frac{3}{5} x^{5} e^{2} d c^{2} b + \frac{2}{5} x^{5} f e c^{3} b + \frac{3}{5} x^{5} e^{2} d^{2} c a + \frac{6}{5} x^{5} f e d c^{2} a + \frac{1}{5} x^{5} f^{2} c^{3} a + \frac{1}{3} x^{3} e^{2} c^{3} b + x^{3} e^{2} d c^{2} a + \frac{2}{3} x^{3} f e c^{3} a + x e^{2} c^{3} a"," ",0,"1/13*x^13*f^2*d^3*b + 2/11*x^11*f*e*d^3*b + 3/11*x^11*f^2*d^2*c*b + 1/11*x^11*f^2*d^3*a + 1/9*x^9*e^2*d^3*b + 2/3*x^9*f*e*d^2*c*b + 1/3*x^9*f^2*d*c^2*b + 2/9*x^9*f*e*d^3*a + 1/3*x^9*f^2*d^2*c*a + 3/7*x^7*e^2*d^2*c*b + 6/7*x^7*f*e*d*c^2*b + 1/7*x^7*f^2*c^3*b + 1/7*x^7*e^2*d^3*a + 6/7*x^7*f*e*d^2*c*a + 3/7*x^7*f^2*d*c^2*a + 3/5*x^5*e^2*d*c^2*b + 2/5*x^5*f*e*c^3*b + 3/5*x^5*e^2*d^2*c*a + 6/5*x^5*f*e*d*c^2*a + 1/5*x^5*f^2*c^3*a + 1/3*x^3*e^2*c^3*b + x^3*e^2*d*c^2*a + 2/3*x^3*f*e*c^3*a + x*e^2*c^3*a","A",0
18,1,165,0,0.848187," ","integrate((b*x^2+a)*(d*x^2+c)^3*(f*x^2+e),x, algorithm=""fricas"")","\frac{1}{11} x^{11} f d^{3} b + \frac{1}{9} x^{9} e d^{3} b + \frac{1}{3} x^{9} f d^{2} c b + \frac{1}{9} x^{9} f d^{3} a + \frac{3}{7} x^{7} e d^{2} c b + \frac{3}{7} x^{7} f d c^{2} b + \frac{1}{7} x^{7} e d^{3} a + \frac{3}{7} x^{7} f d^{2} c a + \frac{3}{5} x^{5} e d c^{2} b + \frac{1}{5} x^{5} f c^{3} b + \frac{3}{5} x^{5} e d^{2} c a + \frac{3}{5} x^{5} f d c^{2} a + \frac{1}{3} x^{3} e c^{3} b + x^{3} e d c^{2} a + \frac{1}{3} x^{3} f c^{3} a + x e c^{3} a"," ",0,"1/11*x^11*f*d^3*b + 1/9*x^9*e*d^3*b + 1/3*x^9*f*d^2*c*b + 1/9*x^9*f*d^3*a + 3/7*x^7*e*d^2*c*b + 3/7*x^7*f*d*c^2*b + 1/7*x^7*e*d^3*a + 3/7*x^7*f*d^2*c*a + 3/5*x^5*e*d*c^2*b + 1/5*x^5*f*c^3*b + 3/5*x^5*e*d^2*c*a + 3/5*x^5*f*d*c^2*a + 1/3*x^3*e*c^3*b + x^3*e*d*c^2*a + 1/3*x^3*f*c^3*a + x*e*c^3*a","A",0
19,1,586,0,1.003946," ","integrate((b*x^2+a)*(d*x^2+c)^3/(f*x^2+e),x, algorithm=""fricas"")","\left[\frac{30 \, b d^{3} e f^{4} x^{7} - 42 \, {\left(b d^{3} e^{2} f^{3} - {\left(3 \, b c d^{2} + a d^{3}\right)} e f^{4}\right)} x^{5} + 70 \, {\left(b d^{3} e^{3} f^{2} - {\left(3 \, b c d^{2} + a d^{3}\right)} e^{2} f^{3} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} e f^{4}\right)} x^{3} - 105 \, {\left(b d^{3} e^{4} + a c^{3} f^{4} - {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f + 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{2} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{3}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) - 210 \, {\left(b d^{3} e^{4} f - {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{2} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{4}\right)} x}{210 \, e f^{5}}, \frac{15 \, b d^{3} e f^{4} x^{7} - 21 \, {\left(b d^{3} e^{2} f^{3} - {\left(3 \, b c d^{2} + a d^{3}\right)} e f^{4}\right)} x^{5} + 35 \, {\left(b d^{3} e^{3} f^{2} - {\left(3 \, b c d^{2} + a d^{3}\right)} e^{2} f^{3} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} e f^{4}\right)} x^{3} + 105 \, {\left(b d^{3} e^{4} + a c^{3} f^{4} - {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f + 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{2} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{3}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) - 105 \, {\left(b d^{3} e^{4} f - {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{2} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{4}\right)} x}{105 \, e f^{5}}\right]"," ",0,"[1/210*(30*b*d^3*e*f^4*x^7 - 42*(b*d^3*e^2*f^3 - (3*b*c*d^2 + a*d^3)*e*f^4)*x^5 + 70*(b*d^3*e^3*f^2 - (3*b*c*d^2 + a*d^3)*e^2*f^3 + 3*(b*c^2*d + a*c*d^2)*e*f^4)*x^3 - 105*(b*d^3*e^4 + a*c^3*f^4 - (3*b*c*d^2 + a*d^3)*e^3*f + 3*(b*c^2*d + a*c*d^2)*e^2*f^2 - (b*c^3 + 3*a*c^2*d)*e*f^3)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) - 210*(b*d^3*e^4*f - (3*b*c*d^2 + a*d^3)*e^3*f^2 + 3*(b*c^2*d + a*c*d^2)*e^2*f^3 - (b*c^3 + 3*a*c^2*d)*e*f^4)*x)/(e*f^5), 1/105*(15*b*d^3*e*f^4*x^7 - 21*(b*d^3*e^2*f^3 - (3*b*c*d^2 + a*d^3)*e*f^4)*x^5 + 35*(b*d^3*e^3*f^2 - (3*b*c*d^2 + a*d^3)*e^2*f^3 + 3*(b*c^2*d + a*c*d^2)*e*f^4)*x^3 + 105*(b*d^3*e^4 + a*c^3*f^4 - (3*b*c*d^2 + a*d^3)*e^3*f + 3*(b*c^2*d + a*c*d^2)*e^2*f^2 - (b*c^3 + 3*a*c^2*d)*e*f^3)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) - 105*(b*d^3*e^4*f - (3*b*c*d^2 + a*d^3)*e^3*f^2 + 3*(b*c^2*d + a*c*d^2)*e^2*f^3 - (b*c^3 + 3*a*c^2*d)*e*f^4)*x)/(e*f^5)]","A",0
20,1,834,0,1.239006," ","integrate((b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^2,x, algorithm=""fricas"")","\left[\frac{12 \, b d^{3} e^{2} f^{4} x^{7} - 4 \, {\left(7 \, b d^{3} e^{3} f^{3} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{2} f^{4}\right)} x^{5} + 20 \, {\left(7 \, b d^{3} e^{4} f^{2} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{3} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{4}\right)} x^{3} + 15 \, {\left(7 \, b d^{3} e^{5} - a c^{3} e f^{4} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{2} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{3} + {\left(7 \, b d^{3} e^{4} f - a c^{3} f^{5} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{2} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{4}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) + 30 \, {\left(7 \, b d^{3} e^{5} f + a c^{3} e f^{5} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{2} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{4}\right)} x}{60 \, {\left(e^{2} f^{6} x^{2} + e^{3} f^{5}\right)}}, \frac{6 \, b d^{3} e^{2} f^{4} x^{7} - 2 \, {\left(7 \, b d^{3} e^{3} f^{3} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{2} f^{4}\right)} x^{5} + 10 \, {\left(7 \, b d^{3} e^{4} f^{2} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{3} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{4}\right)} x^{3} - 15 \, {\left(7 \, b d^{3} e^{5} - a c^{3} e f^{4} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{2} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{3} + {\left(7 \, b d^{3} e^{4} f - a c^{3} f^{5} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{2} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{4}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) + 15 \, {\left(7 \, b d^{3} e^{5} f + a c^{3} e f^{5} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{2} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{4}\right)} x}{30 \, {\left(e^{2} f^{6} x^{2} + e^{3} f^{5}\right)}}\right]"," ",0,"[1/60*(12*b*d^3*e^2*f^4*x^7 - 4*(7*b*d^3*e^3*f^3 - 5*(3*b*c*d^2 + a*d^3)*e^2*f^4)*x^5 + 20*(7*b*d^3*e^4*f^2 - 5*(3*b*c*d^2 + a*d^3)*e^3*f^3 + 9*(b*c^2*d + a*c*d^2)*e^2*f^4)*x^3 + 15*(7*b*d^3*e^5 - a*c^3*e*f^4 - 5*(3*b*c*d^2 + a*d^3)*e^4*f + 9*(b*c^2*d + a*c*d^2)*e^3*f^2 - (b*c^3 + 3*a*c^2*d)*e^2*f^3 + (7*b*d^3*e^4*f - a*c^3*f^5 - 5*(3*b*c*d^2 + a*d^3)*e^3*f^2 + 9*(b*c^2*d + a*c*d^2)*e^2*f^3 - (b*c^3 + 3*a*c^2*d)*e*f^4)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) + 30*(7*b*d^3*e^5*f + a*c^3*e*f^5 - 5*(3*b*c*d^2 + a*d^3)*e^4*f^2 + 9*(b*c^2*d + a*c*d^2)*e^3*f^3 - (b*c^3 + 3*a*c^2*d)*e^2*f^4)*x)/(e^2*f^6*x^2 + e^3*f^5), 1/30*(6*b*d^3*e^2*f^4*x^7 - 2*(7*b*d^3*e^3*f^3 - 5*(3*b*c*d^2 + a*d^3)*e^2*f^4)*x^5 + 10*(7*b*d^3*e^4*f^2 - 5*(3*b*c*d^2 + a*d^3)*e^3*f^3 + 9*(b*c^2*d + a*c*d^2)*e^2*f^4)*x^3 - 15*(7*b*d^3*e^5 - a*c^3*e*f^4 - 5*(3*b*c*d^2 + a*d^3)*e^4*f + 9*(b*c^2*d + a*c*d^2)*e^3*f^2 - (b*c^3 + 3*a*c^2*d)*e^2*f^3 + (7*b*d^3*e^4*f - a*c^3*f^5 - 5*(3*b*c*d^2 + a*d^3)*e^3*f^2 + 9*(b*c^2*d + a*c*d^2)*e^2*f^3 - (b*c^3 + 3*a*c^2*d)*e*f^4)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) + 15*(7*b*d^3*e^5*f + a*c^3*e*f^5 - 5*(3*b*c*d^2 + a*d^3)*e^4*f^2 + 9*(b*c^2*d + a*c*d^2)*e^3*f^3 - (b*c^3 + 3*a*c^2*d)*e^2*f^4)*x)/(e^2*f^6*x^2 + e^3*f^5)]","A",0
21,1,1102,0,1.555923," ","integrate((b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^3,x, algorithm=""fricas"")","\left[\frac{16 \, b d^{3} e^{3} f^{4} x^{7} - 16 \, {\left(7 \, b d^{3} e^{4} f^{3} - 3 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{4}\right)} x^{5} - 2 \, {\left(175 \, b d^{3} e^{5} f^{2} - 9 \, a c^{3} e f^{6} - 75 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{3} + 45 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{4} - 3 \, {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{5}\right)} x^{3} - 3 \, {\left(35 \, b d^{3} e^{6} + 3 \, a c^{3} e^{2} f^{4} - 15 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{5} f + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{4} f^{2} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{3} f^{3} + {\left(35 \, b d^{3} e^{4} f^{2} + 3 \, a c^{3} f^{6} - 15 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{3} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{4} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{5}\right)} x^{4} + 2 \, {\left(35 \, b d^{3} e^{5} f + 3 \, a c^{3} e f^{5} - 15 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{2} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{4}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) - 6 \, {\left(35 \, b d^{3} e^{6} f - 5 \, a c^{3} e^{2} f^{5} - 15 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{5} f^{2} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{4} f^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{3} f^{4}\right)} x}{48 \, {\left(e^{3} f^{7} x^{4} + 2 \, e^{4} f^{6} x^{2} + e^{5} f^{5}\right)}}, \frac{8 \, b d^{3} e^{3} f^{4} x^{7} - 8 \, {\left(7 \, b d^{3} e^{4} f^{3} - 3 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{4}\right)} x^{5} - {\left(175 \, b d^{3} e^{5} f^{2} - 9 \, a c^{3} e f^{6} - 75 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{3} + 45 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{4} - 3 \, {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{5}\right)} x^{3} + 3 \, {\left(35 \, b d^{3} e^{6} + 3 \, a c^{3} e^{2} f^{4} - 15 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{5} f + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{4} f^{2} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{3} f^{3} + {\left(35 \, b d^{3} e^{4} f^{2} + 3 \, a c^{3} f^{6} - 15 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{3} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{4} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{5}\right)} x^{4} + 2 \, {\left(35 \, b d^{3} e^{5} f + 3 \, a c^{3} e f^{5} - 15 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{2} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{4}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) - 3 \, {\left(35 \, b d^{3} e^{6} f - 5 \, a c^{3} e^{2} f^{5} - 15 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{5} f^{2} + 9 \, {\left(b c^{2} d + a c d^{2}\right)} e^{4} f^{3} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{3} f^{4}\right)} x}{24 \, {\left(e^{3} f^{7} x^{4} + 2 \, e^{4} f^{6} x^{2} + e^{5} f^{5}\right)}}\right]"," ",0,"[1/48*(16*b*d^3*e^3*f^4*x^7 - 16*(7*b*d^3*e^4*f^3 - 3*(3*b*c*d^2 + a*d^3)*e^3*f^4)*x^5 - 2*(175*b*d^3*e^5*f^2 - 9*a*c^3*e*f^6 - 75*(3*b*c*d^2 + a*d^3)*e^4*f^3 + 45*(b*c^2*d + a*c*d^2)*e^3*f^4 - 3*(b*c^3 + 3*a*c^2*d)*e^2*f^5)*x^3 - 3*(35*b*d^3*e^6 + 3*a*c^3*e^2*f^4 - 15*(3*b*c*d^2 + a*d^3)*e^5*f + 9*(b*c^2*d + a*c*d^2)*e^4*f^2 + (b*c^3 + 3*a*c^2*d)*e^3*f^3 + (35*b*d^3*e^4*f^2 + 3*a*c^3*f^6 - 15*(3*b*c*d^2 + a*d^3)*e^3*f^3 + 9*(b*c^2*d + a*c*d^2)*e^2*f^4 + (b*c^3 + 3*a*c^2*d)*e*f^5)*x^4 + 2*(35*b*d^3*e^5*f + 3*a*c^3*e*f^5 - 15*(3*b*c*d^2 + a*d^3)*e^4*f^2 + 9*(b*c^2*d + a*c*d^2)*e^3*f^3 + (b*c^3 + 3*a*c^2*d)*e^2*f^4)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) - 6*(35*b*d^3*e^6*f - 5*a*c^3*e^2*f^5 - 15*(3*b*c*d^2 + a*d^3)*e^5*f^2 + 9*(b*c^2*d + a*c*d^2)*e^4*f^3 + (b*c^3 + 3*a*c^2*d)*e^3*f^4)*x)/(e^3*f^7*x^4 + 2*e^4*f^6*x^2 + e^5*f^5), 1/24*(8*b*d^3*e^3*f^4*x^7 - 8*(7*b*d^3*e^4*f^3 - 3*(3*b*c*d^2 + a*d^3)*e^3*f^4)*x^5 - (175*b*d^3*e^5*f^2 - 9*a*c^3*e*f^6 - 75*(3*b*c*d^2 + a*d^3)*e^4*f^3 + 45*(b*c^2*d + a*c*d^2)*e^3*f^4 - 3*(b*c^3 + 3*a*c^2*d)*e^2*f^5)*x^3 + 3*(35*b*d^3*e^6 + 3*a*c^3*e^2*f^4 - 15*(3*b*c*d^2 + a*d^3)*e^5*f + 9*(b*c^2*d + a*c*d^2)*e^4*f^2 + (b*c^3 + 3*a*c^2*d)*e^3*f^3 + (35*b*d^3*e^4*f^2 + 3*a*c^3*f^6 - 15*(3*b*c*d^2 + a*d^3)*e^3*f^3 + 9*(b*c^2*d + a*c*d^2)*e^2*f^4 + (b*c^3 + 3*a*c^2*d)*e*f^5)*x^4 + 2*(35*b*d^3*e^5*f + 3*a*c^3*e*f^5 - 15*(3*b*c*d^2 + a*d^3)*e^4*f^2 + 9*(b*c^2*d + a*c*d^2)*e^3*f^3 + (b*c^3 + 3*a*c^2*d)*e^2*f^4)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) - 3*(35*b*d^3*e^6*f - 5*a*c^3*e^2*f^5 - 15*(3*b*c*d^2 + a*d^3)*e^5*f^2 + 9*(b*c^2*d + a*c*d^2)*e^4*f^3 + (b*c^3 + 3*a*c^2*d)*e^3*f^4)*x)/(e^3*f^7*x^4 + 2*e^4*f^6*x^2 + e^5*f^5)]","A",0
22,1,1422,0,1.381361," ","integrate((b*x^2+a)*(d*x^2+c)^3/(f*x^2+e)^4,x, algorithm=""fricas"")","\left[\frac{96 \, b d^{3} e^{4} f^{4} x^{7} + 6 \, {\left(77 \, b d^{3} e^{5} f^{3} + 5 \, a c^{3} e f^{7} - 11 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{4} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{5} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{6}\right)} x^{5} + 16 \, {\left(35 \, b d^{3} e^{6} f^{2} + 5 \, a c^{3} e^{2} f^{6} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{5} f^{3} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{4} f^{4} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{3} f^{5}\right)} x^{3} + 3 \, {\left(35 \, b d^{3} e^{7} - 5 \, a c^{3} e^{3} f^{4} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{6} f - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{5} f^{2} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{4} f^{3} + {\left(35 \, b d^{3} e^{4} f^{3} - 5 \, a c^{3} f^{7} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{4} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{5} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{6}\right)} x^{6} + 3 \, {\left(35 \, b d^{3} e^{5} f^{2} - 5 \, a c^{3} e f^{6} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{3} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{4} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{5}\right)} x^{4} + 3 \, {\left(35 \, b d^{3} e^{6} f - 5 \, a c^{3} e^{2} f^{5} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{5} f^{2} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{4} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{3} f^{4}\right)} x^{2}\right)} \sqrt{-e f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-e f} x - e}{f x^{2} + e}\right) + 6 \, {\left(35 \, b d^{3} e^{7} f + 11 \, a c^{3} e^{3} f^{5} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{6} f^{2} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{5} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{4} f^{4}\right)} x}{96 \, {\left(e^{4} f^{8} x^{6} + 3 \, e^{5} f^{7} x^{4} + 3 \, e^{6} f^{6} x^{2} + e^{7} f^{5}\right)}}, \frac{48 \, b d^{3} e^{4} f^{4} x^{7} + 3 \, {\left(77 \, b d^{3} e^{5} f^{3} + 5 \, a c^{3} e f^{7} - 11 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{4} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{5} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{6}\right)} x^{5} + 8 \, {\left(35 \, b d^{3} e^{6} f^{2} + 5 \, a c^{3} e^{2} f^{6} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{5} f^{3} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{4} f^{4} + {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{3} f^{5}\right)} x^{3} - 3 \, {\left(35 \, b d^{3} e^{7} - 5 \, a c^{3} e^{3} f^{4} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{6} f - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{5} f^{2} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{4} f^{3} + {\left(35 \, b d^{3} e^{4} f^{3} - 5 \, a c^{3} f^{7} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{3} f^{4} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{2} f^{5} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e f^{6}\right)} x^{6} + 3 \, {\left(35 \, b d^{3} e^{5} f^{2} - 5 \, a c^{3} e f^{6} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{4} f^{3} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{3} f^{4} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{2} f^{5}\right)} x^{4} + 3 \, {\left(35 \, b d^{3} e^{6} f - 5 \, a c^{3} e^{2} f^{5} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{5} f^{2} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{4} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{3} f^{4}\right)} x^{2}\right)} \sqrt{e f} \arctan\left(\frac{\sqrt{e f} x}{e}\right) + 3 \, {\left(35 \, b d^{3} e^{7} f + 11 \, a c^{3} e^{3} f^{5} - 5 \, {\left(3 \, b c d^{2} + a d^{3}\right)} e^{6} f^{2} - 3 \, {\left(b c^{2} d + a c d^{2}\right)} e^{5} f^{3} - {\left(b c^{3} + 3 \, a c^{2} d\right)} e^{4} f^{4}\right)} x}{48 \, {\left(e^{4} f^{8} x^{6} + 3 \, e^{5} f^{7} x^{4} + 3 \, e^{6} f^{6} x^{2} + e^{7} f^{5}\right)}}\right]"," ",0,"[1/96*(96*b*d^3*e^4*f^4*x^7 + 6*(77*b*d^3*e^5*f^3 + 5*a*c^3*e*f^7 - 11*(3*b*c*d^2 + a*d^3)*e^4*f^4 + 3*(b*c^2*d + a*c*d^2)*e^3*f^5 + (b*c^3 + 3*a*c^2*d)*e^2*f^6)*x^5 + 16*(35*b*d^3*e^6*f^2 + 5*a*c^3*e^2*f^6 - 5*(3*b*c*d^2 + a*d^3)*e^5*f^3 - 3*(b*c^2*d + a*c*d^2)*e^4*f^4 + (b*c^3 + 3*a*c^2*d)*e^3*f^5)*x^3 + 3*(35*b*d^3*e^7 - 5*a*c^3*e^3*f^4 - 5*(3*b*c*d^2 + a*d^3)*e^6*f - 3*(b*c^2*d + a*c*d^2)*e^5*f^2 - (b*c^3 + 3*a*c^2*d)*e^4*f^3 + (35*b*d^3*e^4*f^3 - 5*a*c^3*f^7 - 5*(3*b*c*d^2 + a*d^3)*e^3*f^4 - 3*(b*c^2*d + a*c*d^2)*e^2*f^5 - (b*c^3 + 3*a*c^2*d)*e*f^6)*x^6 + 3*(35*b*d^3*e^5*f^2 - 5*a*c^3*e*f^6 - 5*(3*b*c*d^2 + a*d^3)*e^4*f^3 - 3*(b*c^2*d + a*c*d^2)*e^3*f^4 - (b*c^3 + 3*a*c^2*d)*e^2*f^5)*x^4 + 3*(35*b*d^3*e^6*f - 5*a*c^3*e^2*f^5 - 5*(3*b*c*d^2 + a*d^3)*e^5*f^2 - 3*(b*c^2*d + a*c*d^2)*e^4*f^3 - (b*c^3 + 3*a*c^2*d)*e^3*f^4)*x^2)*sqrt(-e*f)*log((f*x^2 - 2*sqrt(-e*f)*x - e)/(f*x^2 + e)) + 6*(35*b*d^3*e^7*f + 11*a*c^3*e^3*f^5 - 5*(3*b*c*d^2 + a*d^3)*e^6*f^2 - 3*(b*c^2*d + a*c*d^2)*e^5*f^3 - (b*c^3 + 3*a*c^2*d)*e^4*f^4)*x)/(e^4*f^8*x^6 + 3*e^5*f^7*x^4 + 3*e^6*f^6*x^2 + e^7*f^5), 1/48*(48*b*d^3*e^4*f^4*x^7 + 3*(77*b*d^3*e^5*f^3 + 5*a*c^3*e*f^7 - 11*(3*b*c*d^2 + a*d^3)*e^4*f^4 + 3*(b*c^2*d + a*c*d^2)*e^3*f^5 + (b*c^3 + 3*a*c^2*d)*e^2*f^6)*x^5 + 8*(35*b*d^3*e^6*f^2 + 5*a*c^3*e^2*f^6 - 5*(3*b*c*d^2 + a*d^3)*e^5*f^3 - 3*(b*c^2*d + a*c*d^2)*e^4*f^4 + (b*c^3 + 3*a*c^2*d)*e^3*f^5)*x^3 - 3*(35*b*d^3*e^7 - 5*a*c^3*e^3*f^4 - 5*(3*b*c*d^2 + a*d^3)*e^6*f - 3*(b*c^2*d + a*c*d^2)*e^5*f^2 - (b*c^3 + 3*a*c^2*d)*e^4*f^3 + (35*b*d^3*e^4*f^3 - 5*a*c^3*f^7 - 5*(3*b*c*d^2 + a*d^3)*e^3*f^4 - 3*(b*c^2*d + a*c*d^2)*e^2*f^5 - (b*c^3 + 3*a*c^2*d)*e*f^6)*x^6 + 3*(35*b*d^3*e^5*f^2 - 5*a*c^3*e*f^6 - 5*(3*b*c*d^2 + a*d^3)*e^4*f^3 - 3*(b*c^2*d + a*c*d^2)*e^3*f^4 - (b*c^3 + 3*a*c^2*d)*e^2*f^5)*x^4 + 3*(35*b*d^3*e^6*f - 5*a*c^3*e^2*f^5 - 5*(3*b*c*d^2 + a*d^3)*e^5*f^2 - 3*(b*c^2*d + a*c*d^2)*e^4*f^3 - (b*c^3 + 3*a*c^2*d)*e^3*f^4)*x^2)*sqrt(e*f)*arctan(sqrt(e*f)*x/e) + 3*(35*b*d^3*e^7*f + 11*a*c^3*e^3*f^5 - 5*(3*b*c*d^2 + a*d^3)*e^6*f^2 - 3*(b*c^2*d + a*c*d^2)*e^5*f^3 - (b*c^3 + 3*a*c^2*d)*e^4*f^4)*x)/(e^4*f^8*x^6 + 3*e^5*f^7*x^4 + 3*e^6*f^6*x^2 + e^7*f^5)]","B",0
23,0,0,0,1.243110," ","integrate((b*x^2+a)*(d*x^2+c)^(3/2)*(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b d x^{4} + {\left(b c + a d\right)} x^{2} + a c\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}, x\right)"," ",0,"integral((b*d*x^4 + (b*c + a*d)*x^2 + a*c)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e), x)","F",0
24,0,0,0,1.204982," ","integrate((b*x^2+a)*(d*x^2+c)^(1/2)*(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e), x)","F",0
25,0,0,0,0.870551," ","integrate((b*x^2+a)*(f*x^2+e)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{f x^{2} + e}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(f*x^2 + e)/sqrt(d*x^2 + c), x)","F",0
26,0,0,0,0.954763," ","integrate((b*x^2+a)*(f*x^2+e)^(1/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
27,0,0,0,1.755751," ","integrate((b*x^2+a)*(f*x^2+e)^(1/2)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
28,0,0,0,1.656007," ","integrate((b*x^2+a)*(f*x^2+e)^(1/2)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{4} x^{8} + 4 \, c d^{3} x^{6} + 6 \, c^{2} d^{2} x^{4} + 4 \, c^{3} d x^{2} + c^{4}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^4*x^8 + 4*c*d^3*x^6 + 6*c^2*d^2*x^4 + 4*c^3*d*x^2 + c^4), x)","F",0
29,0,0,0,1.498998," ","integrate((b*x^2+a)*(d*x^2+c)^(1/2)*(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b f x^{4} + {\left(b e + a f\right)} x^{2} + a e\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}, x\right)"," ",0,"integral((b*f*x^4 + (b*e + a*f)*x^2 + a*e)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e), x)","F",0
30,0,0,0,1.506441," ","integrate((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b f x^{4} + {\left(b e + a f\right)} x^{2} + a e\right)} \sqrt{f x^{2} + e}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b*f*x^4 + (b*e + a*f)*x^2 + a*e)*sqrt(f*x^2 + e)/sqrt(d*x^2 + c), x)","F",0
31,0,0,0,1.245275," ","integrate((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b f x^{4} + {\left(b e + a f\right)} x^{2} + a e\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b*f*x^4 + (b*e + a*f)*x^2 + a*e)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
32,0,0,0,1.661258," ","integrate((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b f x^{4} + {\left(b e + a f\right)} x^{2} + a e\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((b*f*x^4 + (b*e + a*f)*x^2 + a*e)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
33,0,0,0,1.737692," ","integrate((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b f x^{4} + {\left(b e + a f\right)} x^{2} + a e\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{4} x^{8} + 4 \, c d^{3} x^{6} + 6 \, c^{2} d^{2} x^{4} + 4 \, c^{3} d x^{2} + c^{4}}, x\right)"," ",0,"integral((b*f*x^4 + (b*e + a*f)*x^2 + a*e)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^4*x^8 + 4*c*d^3*x^6 + 6*c^2*d^2*x^4 + 4*c^3*d*x^2 + c^4), x)","F",0
34,0,0,0,1.840773," ","integrate((b*x^2+a)*(f*x^2+e)^(3/2)/(d*x^2+c)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b f x^{4} + {\left(b e + a f\right)} x^{2} + a e\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{5} x^{10} + 5 \, c d^{4} x^{8} + 10 \, c^{2} d^{3} x^{6} + 10 \, c^{3} d^{2} x^{4} + 5 \, c^{4} d x^{2} + c^{5}}, x\right)"," ",0,"integral((b*f*x^4 + (b*e + a*f)*x^2 + a*e)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^5*x^10 + 5*c*d^4*x^8 + 10*c^2*d^3*x^6 + 10*c^3*d^2*x^4 + 5*c^4*d*x^2 + c^5), x)","F",0
35,0,0,0,1.168164," ","integrate((b*x^2+a)*(d*x^2+c)^(5/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b d^{2} x^{6} + {\left(2 \, b c d + a d^{2}\right)} x^{4} + a c^{2} + {\left(b c^{2} + 2 \, a c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{\sqrt{f x^{2} + e}}, x\right)"," ",0,"integral((b*d^2*x^6 + (2*b*c*d + a*d^2)*x^4 + a*c^2 + (b*c^2 + 2*a*c*d)*x^2)*sqrt(d*x^2 + c)/sqrt(f*x^2 + e), x)","F",0
36,0,0,0,1.245199," ","integrate((b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b d x^{4} + {\left(b c + a d\right)} x^{2} + a c\right)} \sqrt{d x^{2} + c}}{\sqrt{f x^{2} + e}}, x\right)"," ",0,"integral((b*d*x^4 + (b*c + a*d)*x^2 + a*c)*sqrt(d*x^2 + c)/sqrt(f*x^2 + e), x)","F",0
37,0,0,0,1.488065," ","integrate((b*x^2+a)*(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c}}{\sqrt{f x^{2} + e}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)/sqrt(f*x^2 + e), x)","F",0
38,0,0,0,1.334776," ","integrate((b*x^2+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d f x^{4} + {\left(d e + c f\right)} x^{2} + c e}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d*f*x^4 + (d*e + c*f)*x^2 + c*e), x)","F",0
39,0,0,0,1.521910," ","integrate((b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{2} f x^{6} + {\left(d^{2} e + 2 \, c d f\right)} x^{4} + c^{2} e + {\left(2 \, c d e + c^{2} f\right)} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^2*f*x^6 + (d^2*e + 2*c*d*f)*x^4 + c^2*e + (2*c*d*e + c^2*f)*x^2), x)","F",0
40,0,0,0,1.164605," ","integrate((b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{3} f x^{8} + {\left(d^{3} e + 3 \, c d^{2} f\right)} x^{6} + 3 \, {\left(c d^{2} e + c^{2} d f\right)} x^{4} + c^{3} e + {\left(3 \, c^{2} d e + c^{3} f\right)} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^3*f*x^8 + (d^3*e + 3*c*d^2*f)*x^6 + 3*(c*d^2*e + c^2*d*f)*x^4 + c^3*e + (3*c^2*d*e + c^3*f)*x^2), x)","F",0
41,0,0,0,1.460935," ","integrate((b*x^2+a)/(d*x^2+c)^(7/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{4} f x^{10} + {\left(d^{4} e + 4 \, c d^{3} f\right)} x^{8} + 2 \, {\left(2 \, c d^{3} e + 3 \, c^{2} d^{2} f\right)} x^{6} + c^{4} e + 2 \, {\left(3 \, c^{2} d^{2} e + 2 \, c^{3} d f\right)} x^{4} + {\left(4 \, c^{3} d e + c^{4} f\right)} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^4*f*x^10 + (d^4*e + 4*c*d^3*f)*x^8 + 2*(2*c*d^3*e + 3*c^2*d^2*f)*x^6 + c^4*e + 2*(3*c^2*d^2*e + 2*c^3*d*f)*x^4 + (4*c^3*d*e + c^4*f)*x^2), x)","F",0
42,0,0,0,1.455196," ","integrate((b*x^2+a)*(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b d^{2} x^{6} + {\left(2 \, b c d + a d^{2}\right)} x^{4} + a c^{2} + {\left(b c^{2} + 2 \, a c d\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{f^{2} x^{4} + 2 \, e f x^{2} + e^{2}}, x\right)"," ",0,"integral((b*d^2*x^6 + (2*b*c*d + a*d^2)*x^4 + a*c^2 + (b*c^2 + 2*a*c*d)*x^2)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(f^2*x^4 + 2*e*f*x^2 + e^2), x)","F",0
43,0,0,0,1.119820," ","integrate((b*x^2+a)*(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b d x^{4} + {\left(b c + a d\right)} x^{2} + a c\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{f^{2} x^{4} + 2 \, e f x^{2} + e^{2}}, x\right)"," ",0,"integral((b*d*x^4 + (b*c + a*d)*x^2 + a*c)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(f^2*x^4 + 2*e*f*x^2 + e^2), x)","F",0
44,0,0,0,0.770710," ","integrate((b*x^2+a)*(d*x^2+c)^(1/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{f^{2} x^{4} + 2 \, e f x^{2} + e^{2}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(f^2*x^4 + 2*e*f*x^2 + e^2), x)","F",0
45,0,0,0,1.300289," ","integrate((b*x^2+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d f^{2} x^{6} + {\left(2 \, d e f + c f^{2}\right)} x^{4} + c e^{2} + {\left(d e^{2} + 2 \, c e f\right)} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d*f^2*x^6 + (2*d*e*f + c*f^2)*x^4 + c*e^2 + (d*e^2 + 2*c*e*f)*x^2), x)","F",0
46,0,0,0,1.939442," ","integrate((b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{2} f^{2} x^{8} + 2 \, {\left(d^{2} e f + c d f^{2}\right)} x^{6} + {\left(d^{2} e^{2} + 4 \, c d e f + c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} + 2 \, {\left(c d e^{2} + c^{2} e f\right)} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^2*f^2*x^8 + 2*(d^2*e*f + c*d*f^2)*x^6 + (d^2*e^2 + 4*c*d*e*f + c^2*f^2)*x^4 + c^2*e^2 + 2*(c*d*e^2 + c^2*e*f)*x^2), x)","F",0
47,0,0,0,1.470773," ","integrate((b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{d^{3} f^{2} x^{10} + {\left(2 \, d^{3} e f + 3 \, c d^{2} f^{2}\right)} x^{8} + {\left(d^{3} e^{2} + 6 \, c d^{2} e f + 3 \, c^{2} d f^{2}\right)} x^{6} + c^{3} e^{2} + {\left(3 \, c d^{2} e^{2} + 6 \, c^{2} d e f + c^{3} f^{2}\right)} x^{4} + {\left(3 \, c^{2} d e^{2} + 2 \, c^{3} e f\right)} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(d^3*f^2*x^10 + (2*d^3*e*f + 3*c*d^2*f^2)*x^8 + (d^3*e^2 + 6*c*d^2*e*f + 3*c^2*d*f^2)*x^6 + c^3*e^2 + (3*c*d^2*e^2 + 6*c^2*d*e*f + c^3*f^2)*x^4 + (3*c^2*d*e^2 + 2*c^3*e*f)*x^2), x)","F",0
48,0,0,0,1.365623," ","integrate((f*x^2+e)/(d*x^2+c)^(3/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} {\left(f x^{2} + e\right)}}{b d^{2} x^{6} + {\left(2 \, b c d + a d^{2}\right)} x^{4} + a c^{2} + {\left(b c^{2} + 2 \, a c d\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*(f*x^2 + e)/(b*d^2*x^6 + (2*b*c*d + a*d^2)*x^4 + a*c^2 + (b*c^2 + 2*a*c*d)*x^2), x)","F",0
49,0,0,0,0.884168," ","integrate((f*x^2+e)/(d*x^2+c)^(3/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{d x^{2} + c} {\left(f x^{2} + e\right)}}{b d^{2} x^{6} + {\left(2 \, b c d - a d^{2}\right)} x^{4} - a c^{2} + {\left(b c^{2} - 2 \, a c d\right)} x^{2}}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(d*x^2 + c)*(f*x^2 + e)/(b*d^2*x^6 + (2*b*c*d - a*d^2)*x^4 - a*c^2 + (b*c^2 - 2*a*c*d)*x^2), x)","F",0
50,0,0,0,1.274534," ","integrate((f*x^2+e)/(-d*x^2+c)^(3/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{-d x^{2} + c} {\left(f x^{2} + e\right)}}{b d^{2} x^{6} - {\left(2 \, b c d - a d^{2}\right)} x^{4} + a c^{2} + {\left(b c^{2} - 2 \, a c d\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(-d*x^2 + c)*(f*x^2 + e)/(b*d^2*x^6 - (2*b*c*d - a*d^2)*x^4 + a*c^2 + (b*c^2 - 2*a*c*d)*x^2), x)","F",0
51,0,0,0,1.187024," ","integrate((f*x^2+e)/(-d*x^2+c)^(3/2)/(-b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b x^{2} + a} \sqrt{-d x^{2} + c} {\left(f x^{2} + e\right)}}{b d^{2} x^{6} - {\left(2 \, b c d + a d^{2}\right)} x^{4} - a c^{2} + {\left(b c^{2} + 2 \, a c d\right)} x^{2}}, x\right)"," ",0,"integral(-sqrt(-b*x^2 + a)*sqrt(-d*x^2 + c)*(f*x^2 + e)/(b*d^2*x^6 - (2*b*c*d + a*d^2)*x^4 - a*c^2 + (b*c^2 + 2*a*c*d)*x^2), x)","F",0
52,0,0,0,0.778841," ","integrate((b*x^2+a)/(d*x^2+2)^(1/2)/(f*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + 2} \sqrt{f x^{2} + 3}}{d f x^{4} + {\left(3 \, d + 2 \, f\right)} x^{2} + 6}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + 2)*sqrt(f*x^2 + 3)/(d*f*x^4 + (3*d + 2*f)*x^2 + 6), x)","F",0
53,0,0,0,1.366621," ","integrate((b*x^2+a)*(d*x^2+2)^(1/2)/(f*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + 2}}{\sqrt{f x^{2} + 3}}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + 2)/sqrt(f*x^2 + 3), x)","F",0
54,0,0,0,1.355525," ","integrate((b*x^2+a)*(d*x^2+2)^(1/2)*(f*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)} \sqrt{d x^{2} + 2} \sqrt{f x^{2} + 3}, x\right)"," ",0,"integral((b*x^2 + a)*sqrt(d*x^2 + 2)*sqrt(f*x^2 + 3), x)","F",0
55,0,0,0,1.649989," ","integrate((-b+2*c*x^2-(-4*a*c+b^2)^(1/2))/(1+2*c*x^2/(-b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(-b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, a c x^{2} - a b - \sqrt{b^{2} - 4 \, a c} a\right)} \sqrt{-\frac{b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} - 2 \, a}{a}} \sqrt{-\frac{b x^{2} - \sqrt{b^{2} - 4 \, a c} x^{2} - 2 \, a}{a}}}{2 \, {\left(c x^{4} - b x^{2} + a\right)}}, x\right)"," ",0,"integral(1/2*(2*a*c*x^2 - a*b - sqrt(b^2 - 4*a*c)*a)*sqrt(-(b*x^2 + sqrt(b^2 - 4*a*c)*x^2 - 2*a)/a)*sqrt(-(b*x^2 - sqrt(b^2 - 4*a*c)*x^2 - 2*a)/a)/(c*x^4 - b*x^2 + a), x)","F",0
56,0,0,0,1.423625," ","integrate((2*c*x^2-(-4*a*c+b^2)^(1/2)+b)/(1+2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1+2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, a c x^{2} + a b - \sqrt{b^{2} - 4 \, a c} a\right)} \sqrt{\frac{b x^{2} + \sqrt{b^{2} - 4 \, a c} x^{2} + 2 \, a}{a}} \sqrt{\frac{b x^{2} - \sqrt{b^{2} - 4 \, a c} x^{2} + 2 \, a}{a}}}{2 \, {\left(c x^{4} + b x^{2} + a\right)}}, x\right)"," ",0,"integral(1/2*(2*a*c*x^2 + a*b - sqrt(b^2 - 4*a*c)*a)*sqrt((b*x^2 + sqrt(b^2 - 4*a*c)*x^2 + 2*a)/a)*sqrt((b*x^2 - sqrt(b^2 - 4*a*c)*x^2 + 2*a)/a)/(c*x^4 + b*x^2 + a), x)","F",0
57,1,777,0,4.882161," ","integrate((b*x^2+a)*(d*x^2+c)^(1/2)/(f*x^2+e),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{2} + c} b d f x - {\left(2 \, b d e - {\left(b c + 2 \, a d\right)} f\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - {\left(b d e - a d f\right)} \sqrt{\frac{d e - c f}{e}} \log\left(\frac{{\left(8 \, d^{2} e^{2} - 8 \, c d e f + c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} + 2 \, {\left(4 \, c d e^{2} - 3 \, c^{2} e f\right)} x^{2} - 4 \, {\left(c e^{2} x + {\left(2 \, d e^{2} - c e f\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{d e - c f}{e}}}{f^{2} x^{4} + 2 \, e f x^{2} + e^{2}}\right)}{4 \, d f^{2}}, \frac{2 \, \sqrt{d x^{2} + c} b d f x + 2 \, {\left(2 \, b d e - {\left(b c + 2 \, a d\right)} f\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(b d e - a d f\right)} \sqrt{\frac{d e - c f}{e}} \log\left(\frac{{\left(8 \, d^{2} e^{2} - 8 \, c d e f + c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} + 2 \, {\left(4 \, c d e^{2} - 3 \, c^{2} e f\right)} x^{2} - 4 \, {\left(c e^{2} x + {\left(2 \, d e^{2} - c e f\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{d e - c f}{e}}}{f^{2} x^{4} + 2 \, e f x^{2} + e^{2}}\right)}{4 \, d f^{2}}, \frac{2 \, \sqrt{d x^{2} + c} b d f x - 2 \, {\left(b d e - a d f\right)} \sqrt{-\frac{d e - c f}{e}} \arctan\left(\frac{{\left({\left(2 \, d e - c f\right)} x^{2} + c e\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{d e - c f}{e}}}{2 \, {\left({\left(d^{2} e - c d f\right)} x^{3} + {\left(c d e - c^{2} f\right)} x\right)}}\right) - {\left(2 \, b d e - {\left(b c + 2 \, a d\right)} f\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, d f^{2}}, \frac{\sqrt{d x^{2} + c} b d f x + {\left(2 \, b d e - {\left(b c + 2 \, a d\right)} f\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(b d e - a d f\right)} \sqrt{-\frac{d e - c f}{e}} \arctan\left(\frac{{\left({\left(2 \, d e - c f\right)} x^{2} + c e\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{d e - c f}{e}}}{2 \, {\left({\left(d^{2} e - c d f\right)} x^{3} + {\left(c d e - c^{2} f\right)} x\right)}}\right)}{2 \, d f^{2}}\right]"," ",0,"[1/4*(2*sqrt(d*x^2 + c)*b*d*f*x - (2*b*d*e - (b*c + 2*a*d)*f)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - (b*d*e - a*d*f)*sqrt((d*e - c*f)/e)*log(((8*d^2*e^2 - 8*c*d*e*f + c^2*f^2)*x^4 + c^2*e^2 + 2*(4*c*d*e^2 - 3*c^2*e*f)*x^2 - 4*(c*e^2*x + (2*d*e^2 - c*e*f)*x^3)*sqrt(d*x^2 + c)*sqrt((d*e - c*f)/e))/(f^2*x^4 + 2*e*f*x^2 + e^2)))/(d*f^2), 1/4*(2*sqrt(d*x^2 + c)*b*d*f*x + 2*(2*b*d*e - (b*c + 2*a*d)*f)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (b*d*e - a*d*f)*sqrt((d*e - c*f)/e)*log(((8*d^2*e^2 - 8*c*d*e*f + c^2*f^2)*x^4 + c^2*e^2 + 2*(4*c*d*e^2 - 3*c^2*e*f)*x^2 - 4*(c*e^2*x + (2*d*e^2 - c*e*f)*x^3)*sqrt(d*x^2 + c)*sqrt((d*e - c*f)/e))/(f^2*x^4 + 2*e*f*x^2 + e^2)))/(d*f^2), 1/4*(2*sqrt(d*x^2 + c)*b*d*f*x - 2*(b*d*e - a*d*f)*sqrt(-(d*e - c*f)/e)*arctan(1/2*((2*d*e - c*f)*x^2 + c*e)*sqrt(d*x^2 + c)*sqrt(-(d*e - c*f)/e)/((d^2*e - c*d*f)*x^3 + (c*d*e - c^2*f)*x)) - (2*b*d*e - (b*c + 2*a*d)*f)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(d*f^2), 1/2*(sqrt(d*x^2 + c)*b*d*f*x + (2*b*d*e - (b*c + 2*a*d)*f)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (b*d*e - a*d*f)*sqrt(-(d*e - c*f)/e)*arctan(1/2*((2*d*e - c*f)*x^2 + c*e)*sqrt(d*x^2 + c)*sqrt(-(d*e - c*f)/e)/((d^2*e - c*d*f)*x^3 + (c*d*e - c^2*f)*x)))/(d*f^2)]","A",0
58,1,1718,0,20.972272," ","integrate((b*x^2+a)^3/(d*x^2+c)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-c d e + c^{2} f} f^{3} \log\left(\frac{{\left(d^{2} e^{2} - 8 \, c d e f + 8 \, c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} - 2 \, {\left(3 \, c d e^{2} - 4 \, c^{2} e f\right)} x^{2} - 4 \, {\left({\left(d e - 2 \, c f\right)} x^{3} - c e x\right)} \sqrt{-c d e + c^{2} f} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + {\left(3 \, b^{3} c d^{3} e^{3} + {\left(b^{3} c^{2} d^{2} - 12 \, a b^{2} c d^{3}\right)} e^{2} f + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3}\right)} e f^{2} - 8 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2}\right)} f^{3}\right)} \sqrt{f} \log\left(-2 \, f x^{2} - 2 \, \sqrt{f x^{2} + e} \sqrt{f} x - e\right) + 2 \, {\left(2 \, {\left(b^{3} c d^{3} e f^{2} - b^{3} c^{2} d^{2} f^{3}\right)} x^{3} - {\left(3 \, b^{3} c d^{3} e^{2} f + {\left(b^{3} c^{2} d^{2} - 12 \, a b^{2} c d^{3}\right)} e f^{2} - 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2}\right)} f^{3}\right)} x\right)} \sqrt{f x^{2} + e}}{16 \, {\left(c d^{4} e f^{3} - c^{2} d^{3} f^{4}\right)}}, -\frac{8 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{c d e - c^{2} f} f^{3} \arctan\left(\frac{\sqrt{c d e - c^{2} f} {\left({\left(d e - 2 \, c f\right)} x^{2} - c e\right)} \sqrt{f x^{2} + e}}{2 \, {\left({\left(c d e f - c^{2} f^{2}\right)} x^{3} + {\left(c d e^{2} - c^{2} e f\right)} x\right)}}\right) - {\left(3 \, b^{3} c d^{3} e^{3} + {\left(b^{3} c^{2} d^{2} - 12 \, a b^{2} c d^{3}\right)} e^{2} f + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3}\right)} e f^{2} - 8 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2}\right)} f^{3}\right)} \sqrt{f} \log\left(-2 \, f x^{2} - 2 \, \sqrt{f x^{2} + e} \sqrt{f} x - e\right) - 2 \, {\left(2 \, {\left(b^{3} c d^{3} e f^{2} - b^{3} c^{2} d^{2} f^{3}\right)} x^{3} - {\left(3 \, b^{3} c d^{3} e^{2} f + {\left(b^{3} c^{2} d^{2} - 12 \, a b^{2} c d^{3}\right)} e f^{2} - 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2}\right)} f^{3}\right)} x\right)} \sqrt{f x^{2} + e}}{16 \, {\left(c d^{4} e f^{3} - c^{2} d^{3} f^{4}\right)}}, \frac{2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-c d e + c^{2} f} f^{3} \log\left(\frac{{\left(d^{2} e^{2} - 8 \, c d e f + 8 \, c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} - 2 \, {\left(3 \, c d e^{2} - 4 \, c^{2} e f\right)} x^{2} - 4 \, {\left({\left(d e - 2 \, c f\right)} x^{3} - c e x\right)} \sqrt{-c d e + c^{2} f} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - {\left(3 \, b^{3} c d^{3} e^{3} + {\left(b^{3} c^{2} d^{2} - 12 \, a b^{2} c d^{3}\right)} e^{2} f + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3}\right)} e f^{2} - 8 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2}\right)} f^{3}\right)} \sqrt{-f} \arctan\left(\frac{\sqrt{-f} x}{\sqrt{f x^{2} + e}}\right) + {\left(2 \, {\left(b^{3} c d^{3} e f^{2} - b^{3} c^{2} d^{2} f^{3}\right)} x^{3} - {\left(3 \, b^{3} c d^{3} e^{2} f + {\left(b^{3} c^{2} d^{2} - 12 \, a b^{2} c d^{3}\right)} e f^{2} - 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2}\right)} f^{3}\right)} x\right)} \sqrt{f x^{2} + e}}{8 \, {\left(c d^{4} e f^{3} - c^{2} d^{3} f^{4}\right)}}, -\frac{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{c d e - c^{2} f} f^{3} \arctan\left(\frac{\sqrt{c d e - c^{2} f} {\left({\left(d e - 2 \, c f\right)} x^{2} - c e\right)} \sqrt{f x^{2} + e}}{2 \, {\left({\left(c d e f - c^{2} f^{2}\right)} x^{3} + {\left(c d e^{2} - c^{2} e f\right)} x\right)}}\right) + {\left(3 \, b^{3} c d^{3} e^{3} + {\left(b^{3} c^{2} d^{2} - 12 \, a b^{2} c d^{3}\right)} e^{2} f + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3}\right)} e f^{2} - 8 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2}\right)} f^{3}\right)} \sqrt{-f} \arctan\left(\frac{\sqrt{-f} x}{\sqrt{f x^{2} + e}}\right) - {\left(2 \, {\left(b^{3} c d^{3} e f^{2} - b^{3} c^{2} d^{2} f^{3}\right)} x^{3} - {\left(3 \, b^{3} c d^{3} e^{2} f + {\left(b^{3} c^{2} d^{2} - 12 \, a b^{2} c d^{3}\right)} e f^{2} - 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2}\right)} f^{3}\right)} x\right)} \sqrt{f x^{2} + e}}{8 \, {\left(c d^{4} e f^{3} - c^{2} d^{3} f^{4}\right)}}\right]"," ",0,"[1/16*(4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-c*d*e + c^2*f)*f^3*log(((d^2*e^2 - 8*c*d*e*f + 8*c^2*f^2)*x^4 + c^2*e^2 - 2*(3*c*d*e^2 - 4*c^2*e*f)*x^2 - 4*((d*e - 2*c*f)*x^3 - c*e*x)*sqrt(-c*d*e + c^2*f)*sqrt(f*x^2 + e))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + (3*b^3*c*d^3*e^3 + (b^3*c^2*d^2 - 12*a*b^2*c*d^3)*e^2*f + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3)*e*f^2 - 8*(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2)*f^3)*sqrt(f)*log(-2*f*x^2 - 2*sqrt(f*x^2 + e)*sqrt(f)*x - e) + 2*(2*(b^3*c*d^3*e*f^2 - b^3*c^2*d^2*f^3)*x^3 - (3*b^3*c*d^3*e^2*f + (b^3*c^2*d^2 - 12*a*b^2*c*d^3)*e*f^2 - 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2)*f^3)*x)*sqrt(f*x^2 + e))/(c*d^4*e*f^3 - c^2*d^3*f^4), -1/16*(8*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(c*d*e - c^2*f)*f^3*arctan(1/2*sqrt(c*d*e - c^2*f)*((d*e - 2*c*f)*x^2 - c*e)*sqrt(f*x^2 + e)/((c*d*e*f - c^2*f^2)*x^3 + (c*d*e^2 - c^2*e*f)*x)) - (3*b^3*c*d^3*e^3 + (b^3*c^2*d^2 - 12*a*b^2*c*d^3)*e^2*f + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3)*e*f^2 - 8*(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2)*f^3)*sqrt(f)*log(-2*f*x^2 - 2*sqrt(f*x^2 + e)*sqrt(f)*x - e) - 2*(2*(b^3*c*d^3*e*f^2 - b^3*c^2*d^2*f^3)*x^3 - (3*b^3*c*d^3*e^2*f + (b^3*c^2*d^2 - 12*a*b^2*c*d^3)*e*f^2 - 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2)*f^3)*x)*sqrt(f*x^2 + e))/(c*d^4*e*f^3 - c^2*d^3*f^4), 1/8*(2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-c*d*e + c^2*f)*f^3*log(((d^2*e^2 - 8*c*d*e*f + 8*c^2*f^2)*x^4 + c^2*e^2 - 2*(3*c*d*e^2 - 4*c^2*e*f)*x^2 - 4*((d*e - 2*c*f)*x^3 - c*e*x)*sqrt(-c*d*e + c^2*f)*sqrt(f*x^2 + e))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - (3*b^3*c*d^3*e^3 + (b^3*c^2*d^2 - 12*a*b^2*c*d^3)*e^2*f + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3)*e*f^2 - 8*(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2)*f^3)*sqrt(-f)*arctan(sqrt(-f)*x/sqrt(f*x^2 + e)) + (2*(b^3*c*d^3*e*f^2 - b^3*c^2*d^2*f^3)*x^3 - (3*b^3*c*d^3*e^2*f + (b^3*c^2*d^2 - 12*a*b^2*c*d^3)*e*f^2 - 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2)*f^3)*x)*sqrt(f*x^2 + e))/(c*d^4*e*f^3 - c^2*d^3*f^4), -1/8*(4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(c*d*e - c^2*f)*f^3*arctan(1/2*sqrt(c*d*e - c^2*f)*((d*e - 2*c*f)*x^2 - c*e)*sqrt(f*x^2 + e)/((c*d*e*f - c^2*f^2)*x^3 + (c*d*e^2 - c^2*e*f)*x)) + (3*b^3*c*d^3*e^3 + (b^3*c^2*d^2 - 12*a*b^2*c*d^3)*e^2*f + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3)*e*f^2 - 8*(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2)*f^3)*sqrt(-f)*arctan(sqrt(-f)*x/sqrt(f*x^2 + e)) - (2*(b^3*c*d^3*e*f^2 - b^3*c^2*d^2*f^3)*x^3 - (3*b^3*c*d^3*e^2*f + (b^3*c^2*d^2 - 12*a*b^2*c*d^3)*e*f^2 - 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2)*f^3)*x)*sqrt(f*x^2 + e))/(c*d^4*e*f^3 - c^2*d^3*f^4)]","A",0
59,1,1111,0,6.223664," ","integrate((b*x^2+a)^2/(d*x^2+c)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-c d e + c^{2} f} f^{2} \log\left(\frac{{\left(d^{2} e^{2} - 8 \, c d e f + 8 \, c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} - 2 \, {\left(3 \, c d e^{2} - 4 \, c^{2} e f\right)} x^{2} - 4 \, {\left({\left(d e - 2 \, c f\right)} x^{3} - c e x\right)} \sqrt{-c d e + c^{2} f} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - 2 \, {\left(b^{2} c d^{2} e f - b^{2} c^{2} d f^{2}\right)} \sqrt{f x^{2} + e} x + {\left(b^{2} c d^{2} e^{2} + {\left(b^{2} c^{2} d - 4 \, a b c d^{2}\right)} e f - 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d\right)} f^{2}\right)} \sqrt{f} \log\left(-2 \, f x^{2} - 2 \, \sqrt{f x^{2} + e} \sqrt{f} x - e\right)}{4 \, {\left(c d^{3} e f^{2} - c^{2} d^{2} f^{3}\right)}}, \frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d e - c^{2} f} f^{2} \arctan\left(\frac{\sqrt{c d e - c^{2} f} {\left({\left(d e - 2 \, c f\right)} x^{2} - c e\right)} \sqrt{f x^{2} + e}}{2 \, {\left({\left(c d e f - c^{2} f^{2}\right)} x^{3} + {\left(c d e^{2} - c^{2} e f\right)} x\right)}}\right) + 2 \, {\left(b^{2} c d^{2} e f - b^{2} c^{2} d f^{2}\right)} \sqrt{f x^{2} + e} x - {\left(b^{2} c d^{2} e^{2} + {\left(b^{2} c^{2} d - 4 \, a b c d^{2}\right)} e f - 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d\right)} f^{2}\right)} \sqrt{f} \log\left(-2 \, f x^{2} - 2 \, \sqrt{f x^{2} + e} \sqrt{f} x - e\right)}{4 \, {\left(c d^{3} e f^{2} - c^{2} d^{2} f^{3}\right)}}, -\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-c d e + c^{2} f} f^{2} \log\left(\frac{{\left(d^{2} e^{2} - 8 \, c d e f + 8 \, c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} - 2 \, {\left(3 \, c d e^{2} - 4 \, c^{2} e f\right)} x^{2} - 4 \, {\left({\left(d e - 2 \, c f\right)} x^{3} - c e x\right)} \sqrt{-c d e + c^{2} f} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - 2 \, {\left(b^{2} c d^{2} e f - b^{2} c^{2} d f^{2}\right)} \sqrt{f x^{2} + e} x - 2 \, {\left(b^{2} c d^{2} e^{2} + {\left(b^{2} c^{2} d - 4 \, a b c d^{2}\right)} e f - 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d\right)} f^{2}\right)} \sqrt{-f} \arctan\left(\frac{\sqrt{-f} x}{\sqrt{f x^{2} + e}}\right)}{4 \, {\left(c d^{3} e f^{2} - c^{2} d^{2} f^{3}\right)}}, \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d e - c^{2} f} f^{2} \arctan\left(\frac{\sqrt{c d e - c^{2} f} {\left({\left(d e - 2 \, c f\right)} x^{2} - c e\right)} \sqrt{f x^{2} + e}}{2 \, {\left({\left(c d e f - c^{2} f^{2}\right)} x^{3} + {\left(c d e^{2} - c^{2} e f\right)} x\right)}}\right) + {\left(b^{2} c d^{2} e f - b^{2} c^{2} d f^{2}\right)} \sqrt{f x^{2} + e} x + {\left(b^{2} c d^{2} e^{2} + {\left(b^{2} c^{2} d - 4 \, a b c d^{2}\right)} e f - 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d\right)} f^{2}\right)} \sqrt{-f} \arctan\left(\frac{\sqrt{-f} x}{\sqrt{f x^{2} + e}}\right)}{2 \, {\left(c d^{3} e f^{2} - c^{2} d^{2} f^{3}\right)}}\right]"," ",0,"[-1/4*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c*d*e + c^2*f)*f^2*log(((d^2*e^2 - 8*c*d*e*f + 8*c^2*f^2)*x^4 + c^2*e^2 - 2*(3*c*d*e^2 - 4*c^2*e*f)*x^2 - 4*((d*e - 2*c*f)*x^3 - c*e*x)*sqrt(-c*d*e + c^2*f)*sqrt(f*x^2 + e))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - 2*(b^2*c*d^2*e*f - b^2*c^2*d*f^2)*sqrt(f*x^2 + e)*x + (b^2*c*d^2*e^2 + (b^2*c^2*d - 4*a*b*c*d^2)*e*f - 2*(b^2*c^3 - 2*a*b*c^2*d)*f^2)*sqrt(f)*log(-2*f*x^2 - 2*sqrt(f*x^2 + e)*sqrt(f)*x - e))/(c*d^3*e*f^2 - c^2*d^2*f^3), 1/4*(2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d*e - c^2*f)*f^2*arctan(1/2*sqrt(c*d*e - c^2*f)*((d*e - 2*c*f)*x^2 - c*e)*sqrt(f*x^2 + e)/((c*d*e*f - c^2*f^2)*x^3 + (c*d*e^2 - c^2*e*f)*x)) + 2*(b^2*c*d^2*e*f - b^2*c^2*d*f^2)*sqrt(f*x^2 + e)*x - (b^2*c*d^2*e^2 + (b^2*c^2*d - 4*a*b*c*d^2)*e*f - 2*(b^2*c^3 - 2*a*b*c^2*d)*f^2)*sqrt(f)*log(-2*f*x^2 - 2*sqrt(f*x^2 + e)*sqrt(f)*x - e))/(c*d^3*e*f^2 - c^2*d^2*f^3), -1/4*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c*d*e + c^2*f)*f^2*log(((d^2*e^2 - 8*c*d*e*f + 8*c^2*f^2)*x^4 + c^2*e^2 - 2*(3*c*d*e^2 - 4*c^2*e*f)*x^2 - 4*((d*e - 2*c*f)*x^3 - c*e*x)*sqrt(-c*d*e + c^2*f)*sqrt(f*x^2 + e))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - 2*(b^2*c*d^2*e*f - b^2*c^2*d*f^2)*sqrt(f*x^2 + e)*x - 2*(b^2*c*d^2*e^2 + (b^2*c^2*d - 4*a*b*c*d^2)*e*f - 2*(b^2*c^3 - 2*a*b*c^2*d)*f^2)*sqrt(-f)*arctan(sqrt(-f)*x/sqrt(f*x^2 + e)))/(c*d^3*e*f^2 - c^2*d^2*f^3), 1/2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d*e - c^2*f)*f^2*arctan(1/2*sqrt(c*d*e - c^2*f)*((d*e - 2*c*f)*x^2 - c*e)*sqrt(f*x^2 + e)/((c*d*e*f - c^2*f^2)*x^3 + (c*d*e^2 - c^2*e*f)*x)) + (b^2*c*d^2*e*f - b^2*c^2*d*f^2)*sqrt(f*x^2 + e)*x + (b^2*c*d^2*e^2 + (b^2*c^2*d - 4*a*b*c*d^2)*e*f - 2*(b^2*c^3 - 2*a*b*c^2*d)*f^2)*sqrt(-f)*arctan(sqrt(-f)*x/sqrt(f*x^2 + e)))/(c*d^3*e*f^2 - c^2*d^2*f^3)]","A",0
60,1,737,0,4.139672," ","integrate((b*x^2+a)/(d*x^2+c)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-c d e + c^{2} f} {\left(b c - a d\right)} f \log\left(\frac{{\left(d^{2} e^{2} - 8 \, c d e f + 8 \, c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} - 2 \, {\left(3 \, c d e^{2} - 4 \, c^{2} e f\right)} x^{2} - 4 \, {\left({\left(d e - 2 \, c f\right)} x^{3} - c e x\right)} \sqrt{-c d e + c^{2} f} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) + 2 \, {\left(b c d e - b c^{2} f\right)} \sqrt{f} \log\left(-2 \, f x^{2} - 2 \, \sqrt{f x^{2} + e} \sqrt{f} x - e\right)}{4 \, {\left(c d^{2} e f - c^{2} d f^{2}\right)}}, -\frac{\sqrt{c d e - c^{2} f} {\left(b c - a d\right)} f \arctan\left(\frac{\sqrt{c d e - c^{2} f} {\left({\left(d e - 2 \, c f\right)} x^{2} - c e\right)} \sqrt{f x^{2} + e}}{2 \, {\left({\left(c d e f - c^{2} f^{2}\right)} x^{3} + {\left(c d e^{2} - c^{2} e f\right)} x\right)}}\right) - {\left(b c d e - b c^{2} f\right)} \sqrt{f} \log\left(-2 \, f x^{2} - 2 \, \sqrt{f x^{2} + e} \sqrt{f} x - e\right)}{2 \, {\left(c d^{2} e f - c^{2} d f^{2}\right)}}, \frac{\sqrt{-c d e + c^{2} f} {\left(b c - a d\right)} f \log\left(\frac{{\left(d^{2} e^{2} - 8 \, c d e f + 8 \, c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} - 2 \, {\left(3 \, c d e^{2} - 4 \, c^{2} e f\right)} x^{2} - 4 \, {\left({\left(d e - 2 \, c f\right)} x^{3} - c e x\right)} \sqrt{-c d e + c^{2} f} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right) - 4 \, {\left(b c d e - b c^{2} f\right)} \sqrt{-f} \arctan\left(\frac{\sqrt{-f} x}{\sqrt{f x^{2} + e}}\right)}{4 \, {\left(c d^{2} e f - c^{2} d f^{2}\right)}}, -\frac{\sqrt{c d e - c^{2} f} {\left(b c - a d\right)} f \arctan\left(\frac{\sqrt{c d e - c^{2} f} {\left({\left(d e - 2 \, c f\right)} x^{2} - c e\right)} \sqrt{f x^{2} + e}}{2 \, {\left({\left(c d e f - c^{2} f^{2}\right)} x^{3} + {\left(c d e^{2} - c^{2} e f\right)} x\right)}}\right) + 2 \, {\left(b c d e - b c^{2} f\right)} \sqrt{-f} \arctan\left(\frac{\sqrt{-f} x}{\sqrt{f x^{2} + e}}\right)}{2 \, {\left(c d^{2} e f - c^{2} d f^{2}\right)}}\right]"," ",0,"[1/4*(sqrt(-c*d*e + c^2*f)*(b*c - a*d)*f*log(((d^2*e^2 - 8*c*d*e*f + 8*c^2*f^2)*x^4 + c^2*e^2 - 2*(3*c*d*e^2 - 4*c^2*e*f)*x^2 - 4*((d*e - 2*c*f)*x^3 - c*e*x)*sqrt(-c*d*e + c^2*f)*sqrt(f*x^2 + e))/(d^2*x^4 + 2*c*d*x^2 + c^2)) + 2*(b*c*d*e - b*c^2*f)*sqrt(f)*log(-2*f*x^2 - 2*sqrt(f*x^2 + e)*sqrt(f)*x - e))/(c*d^2*e*f - c^2*d*f^2), -1/2*(sqrt(c*d*e - c^2*f)*(b*c - a*d)*f*arctan(1/2*sqrt(c*d*e - c^2*f)*((d*e - 2*c*f)*x^2 - c*e)*sqrt(f*x^2 + e)/((c*d*e*f - c^2*f^2)*x^3 + (c*d*e^2 - c^2*e*f)*x)) - (b*c*d*e - b*c^2*f)*sqrt(f)*log(-2*f*x^2 - 2*sqrt(f*x^2 + e)*sqrt(f)*x - e))/(c*d^2*e*f - c^2*d*f^2), 1/4*(sqrt(-c*d*e + c^2*f)*(b*c - a*d)*f*log(((d^2*e^2 - 8*c*d*e*f + 8*c^2*f^2)*x^4 + c^2*e^2 - 2*(3*c*d*e^2 - 4*c^2*e*f)*x^2 - 4*((d*e - 2*c*f)*x^3 - c*e*x)*sqrt(-c*d*e + c^2*f)*sqrt(f*x^2 + e))/(d^2*x^4 + 2*c*d*x^2 + c^2)) - 4*(b*c*d*e - b*c^2*f)*sqrt(-f)*arctan(sqrt(-f)*x/sqrt(f*x^2 + e)))/(c*d^2*e*f - c^2*d*f^2), -1/2*(sqrt(c*d*e - c^2*f)*(b*c - a*d)*f*arctan(1/2*sqrt(c*d*e - c^2*f)*((d*e - 2*c*f)*x^2 - c*e)*sqrt(f*x^2 + e)/((c*d*e*f - c^2*f^2)*x^3 + (c*d*e^2 - c^2*e*f)*x)) + 2*(b*c*d*e - b*c^2*f)*sqrt(-f)*arctan(sqrt(-f)*x/sqrt(f*x^2 + e)))/(c*d^2*e*f - c^2*d*f^2)]","B",0
61,1,241,0,1.559073," ","integrate(1/(d*x^2+c)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-c d e + c^{2} f} \log\left(\frac{{\left(d^{2} e^{2} - 8 \, c d e f + 8 \, c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} - 2 \, {\left(3 \, c d e^{2} - 4 \, c^{2} e f\right)} x^{2} - 4 \, {\left({\left(d e - 2 \, c f\right)} x^{3} - c e x\right)} \sqrt{-c d e + c^{2} f} \sqrt{f x^{2} + e}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}\right)}{4 \, {\left(c d e - c^{2} f\right)}}, \frac{\arctan\left(\frac{\sqrt{c d e - c^{2} f} {\left({\left(d e - 2 \, c f\right)} x^{2} - c e\right)} \sqrt{f x^{2} + e}}{2 \, {\left({\left(c d e f - c^{2} f^{2}\right)} x^{3} + {\left(c d e^{2} - c^{2} e f\right)} x\right)}}\right)}{2 \, \sqrt{c d e - c^{2} f}}\right]"," ",0,"[-1/4*sqrt(-c*d*e + c^2*f)*log(((d^2*e^2 - 8*c*d*e*f + 8*c^2*f^2)*x^4 + c^2*e^2 - 2*(3*c*d*e^2 - 4*c^2*e*f)*x^2 - 4*((d*e - 2*c*f)*x^3 - c*e*x)*sqrt(-c*d*e + c^2*f)*sqrt(f*x^2 + e))/(d^2*x^4 + 2*c*d*x^2 + c^2))/(c*d*e - c^2*f), 1/2*arctan(1/2*sqrt(c*d*e - c^2*f)*((d*e - 2*c*f)*x^2 - c*e)*sqrt(f*x^2 + e)/((c*d*e*f - c^2*f^2)*x^3 + (c*d*e^2 - c^2*e*f)*x))/sqrt(c*d*e - c^2*f)]","B",0
62,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)*(f*x^2+e)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)*(f*x^2+e)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-1,0,0,0.000000," ","integrate((f*x^2+e)^(1/2)/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate((f*x^2+e)^(1/2)/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate((f*x^2+e)^(1/2)/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate((f*x^2+e)^(1/2)/(b*x^2+a)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)*(f*x^2+e)^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*(f*x^2+e)^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate((f*x^2+e)^(3/2)/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate((f*x^2+e)^(3/2)/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate((f*x^2+e)^(3/2)/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate((f*x^2+e)^(3/2)/(b*x^2+a)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/(b*x^2+a)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/(b*x^2+a)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(3/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(5/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,0,0,0,31.093033," ","integrate((x^2+1)^(3/2)*(x^2+2)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 2} {\left(x^{2} + 1\right)}^{\frac{3}{2}}}{b x^{2} + a}, x\right)"," ",0,"integral(sqrt(x^2 + 2)*(x^2 + 1)^(3/2)/(b*x^2 + a), x)","F",0
90,0,0,0,2.606383," ","integrate((x^2+1)^(1/2)*(x^2+2)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 2} \sqrt{x^{2} + 1}}{b x^{2} + a}, x\right)"," ",0,"integral(sqrt(x^2 + 2)*sqrt(x^2 + 1)/(b*x^2 + a), x)","F",0
91,0,0,0,32.095361," ","integrate((x^2+2)^(1/2)/(x^2+1)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 2} \sqrt{x^{2} + 1}}{b x^{4} + {\left(a + b\right)} x^{2} + a}, x\right)"," ",0,"integral(sqrt(x^2 + 2)*sqrt(x^2 + 1)/(b*x^4 + (a + b)*x^2 + a), x)","F",0
92,0,0,0,35.165657," ","integrate((x^2+2)^(1/2)/(x^2+1)^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 2} \sqrt{x^{2} + 1}}{b x^{6} + {\left(a + 2 \, b\right)} x^{4} + {\left(2 \, a + b\right)} x^{2} + a}, x\right)"," ",0,"integral(sqrt(x^2 + 2)*sqrt(x^2 + 1)/(b*x^6 + (a + 2*b)*x^4 + (2*a + b)*x^2 + a), x)","F",0
93,0,0,0,37.166696," ","integrate((x^2+2)^(1/2)/(x^2+1)^(5/2)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} + 2} \sqrt{x^{2} + 1}}{b x^{8} + {\left(a + 3 \, b\right)} x^{6} + 3 \, {\left(a + b\right)} x^{4} + {\left(3 \, a + b\right)} x^{2} + a}, x\right)"," ",0,"integral(sqrt(x^2 + 2)*sqrt(x^2 + 1)/(b*x^8 + (a + 3*b)*x^6 + 3*(a + b)*x^4 + (3*a + b)*x^2 + a), x)","F",0
94,-1,0,0,0.000000," ","integrate((d*x^2+2)^(1/2)*(f*x^2+3)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((d*x^2+2)^(1/2)/(b*x^2+a)/(f*x^2+3)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+2)^(1/2)/(f*x^2+3)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,0,0,0,0.712886," ","integrate((-x^2+1)^(1/2)/(x^2-1)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{-x^{2} + 1}}{b x^{4} + {\left(a - b\right)} x^{2} - a}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(-x^2 + 1)/(b*x^4 + (a - b)*x^2 - a), x)","F",0
98,1,513,0,5.765085," ","integrate((b*x^2+a)/(f*x^2+e)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b d e^{3} + a c e f^{2} - {\left(b c + a d\right)} e^{2} f\right)} \sqrt{d x^{2} + c} x - {\left(a c e f + {\left(b c - 2 \, a d\right)} e^{2} + {\left(a c f^{2} + {\left(b c - 2 \, a d\right)} e f\right)} x^{2}\right)} \sqrt{d e^{2} - c e f} \log\left(\frac{{\left(8 \, d^{2} e^{2} - 8 \, c d e f + c^{2} f^{2}\right)} x^{4} + c^{2} e^{2} + 2 \, {\left(4 \, c d e^{2} - 3 \, c^{2} e f\right)} x^{2} + 4 \, {\left({\left(2 \, d e - c f\right)} x^{3} + c e x\right)} \sqrt{d e^{2} - c e f} \sqrt{d x^{2} + c}}{f^{2} x^{4} + 2 \, e f x^{2} + e^{2}}\right)}{8 \, {\left(d^{2} e^{5} - 2 \, c d e^{4} f + c^{2} e^{3} f^{2} + {\left(d^{2} e^{4} f - 2 \, c d e^{3} f^{2} + c^{2} e^{2} f^{3}\right)} x^{2}\right)}}, \frac{2 \, {\left(b d e^{3} + a c e f^{2} - {\left(b c + a d\right)} e^{2} f\right)} \sqrt{d x^{2} + c} x + {\left(a c e f + {\left(b c - 2 \, a d\right)} e^{2} + {\left(a c f^{2} + {\left(b c - 2 \, a d\right)} e f\right)} x^{2}\right)} \sqrt{-d e^{2} + c e f} \arctan\left(\frac{\sqrt{-d e^{2} + c e f} {\left({\left(2 \, d e - c f\right)} x^{2} + c e\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(d^{2} e^{2} - c d e f\right)} x^{3} + {\left(c d e^{2} - c^{2} e f\right)} x\right)}}\right)}{4 \, {\left(d^{2} e^{5} - 2 \, c d e^{4} f + c^{2} e^{3} f^{2} + {\left(d^{2} e^{4} f - 2 \, c d e^{3} f^{2} + c^{2} e^{2} f^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(4*(b*d*e^3 + a*c*e*f^2 - (b*c + a*d)*e^2*f)*sqrt(d*x^2 + c)*x - (a*c*e*f + (b*c - 2*a*d)*e^2 + (a*c*f^2 + (b*c - 2*a*d)*e*f)*x^2)*sqrt(d*e^2 - c*e*f)*log(((8*d^2*e^2 - 8*c*d*e*f + c^2*f^2)*x^4 + c^2*e^2 + 2*(4*c*d*e^2 - 3*c^2*e*f)*x^2 + 4*((2*d*e - c*f)*x^3 + c*e*x)*sqrt(d*e^2 - c*e*f)*sqrt(d*x^2 + c))/(f^2*x^4 + 2*e*f*x^2 + e^2)))/(d^2*e^5 - 2*c*d*e^4*f + c^2*e^3*f^2 + (d^2*e^4*f - 2*c*d*e^3*f^2 + c^2*e^2*f^3)*x^2), 1/4*(2*(b*d*e^3 + a*c*e*f^2 - (b*c + a*d)*e^2*f)*sqrt(d*x^2 + c)*x + (a*c*e*f + (b*c - 2*a*d)*e^2 + (a*c*f^2 + (b*c - 2*a*d)*e*f)*x^2)*sqrt(-d*e^2 + c*e*f)*arctan(1/2*sqrt(-d*e^2 + c*e*f)*((2*d*e - c*f)*x^2 + c*e)*sqrt(d*x^2 + c)/((d^2*e^2 - c*d*e*f)*x^3 + (c*d*e^2 - c^2*e*f)*x)))/(d^2*e^5 - 2*c*d*e^4*f + c^2*e^3*f^2 + (d^2*e^4*f - 2*c*d*e^3*f^2 + c^2*e^2*f^3)*x^2)]","B",0
99,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(-d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,0,0,0,1.601950," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(3/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{b^{2} f x^{6} + {\left(b^{2} e + 2 \, a b f\right)} x^{4} + a^{2} e + {\left(2 \, a b e + a^{2} f\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(b^2*f*x^6 + (b^2*e + 2*a*b*f)*x^4 + a^2*e + (2*a*b*e + a^2*f)*x^2), x)","F",0
107,-1,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^(1/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,0,0,0,1.934450," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{b f^{2} x^{6} + {\left(2 \, b e f + a f^{2}\right)} x^{4} + a e^{2} + {\left(b e^{2} + 2 \, a e f\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(b*f^2*x^6 + (2*b*e*f + a*f^2)*x^4 + a*e^2 + (b*e^2 + 2*a*e*f)*x^2), x)","F",0
110,0,0,0,1.763469," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(3/2)/(f*x^2+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{b^{2} f^{2} x^{8} + 2 \, {\left(b^{2} e f + a b f^{2}\right)} x^{6} + {\left(b^{2} e^{2} + 4 \, a b e f + a^{2} f^{2}\right)} x^{4} + a^{2} e^{2} + 2 \, {\left(a b e^{2} + a^{2} e f\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(b^2*f^2*x^8 + 2*(b^2*e*f + a*b*f^2)*x^6 + (b^2*e^2 + 4*a*b*e*f + a^2*f^2)*x^4 + a^2*e^2 + 2*(a*b*e^2 + a^2*e*f)*x^2), x)","F",0
111,-1,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*(f*x^2+e)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,0,0,0,2.026699," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{b d f x^{6} + {\left(b d e + {\left(b c + a d\right)} f\right)} x^{4} + a c e + {\left(a c f + {\left(b c + a d\right)} e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(b*d*f*x^6 + (b*d*e + (b*c + a*d)*f)*x^4 + a*c*e + (a*c*f + (b*c + a*d)*e)*x^2), x)","F",0
115,0,0,0,1.219642," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{f x^{2} + e}}{b^{2} d f x^{8} + {\left(b^{2} d e + {\left(b^{2} c + 2 \, a b d\right)} f\right)} x^{6} + {\left({\left(b^{2} c + 2 \, a b d\right)} e + {\left(2 \, a b c + a^{2} d\right)} f\right)} x^{4} + a^{2} c e + {\left(a^{2} c f + {\left(2 \, a b c + a^{2} d\right)} e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(f*x^2 + e)/(b^2*d*f*x^8 + (b^2*d*e + (b^2*c + 2*a*b*d)*f)*x^6 + ((b^2*c + 2*a*b*d)*e + (2*a*b*c + a^2*d)*f)*x^4 + a^2*c*e + (a^2*c*f + (2*a*b*c + a^2*d)*e)*x^2), x)","F",0
